You'll arrive at Riga International Airport. It's quite small and easy to navigate, so you'll be out in under 10 minutes (unless you have checked baggage). 

• Right outside the exit, you'll find the taxi stand and the stop for bus no. 22, which serves as the airport shuttle. 
• Buy your ticket at the machine right at the stop. Tickets are valid for the entire public transport network, so if you know you'll be using public transit during your stay, you can buy a multi-day pass right away. If not, a 90-minute ticket will be enough.
• For the quickest route to the Old Town, get off at the Grēcinieku iela stop.

NOTE: You need to tap your ticket against the reader on the bus to validate it. You don't "punch" it, just tap it, and a green light will let you know if the validation was successful.

Just a few steps after getting off the bus, you'll stumble upon perhaps the most famous and photogenic landmark in Riga - the House of the Blackheads. Built in 1334, the house is often called the heart of Riga, and from the very beginning, it served to receive important guests, which is immediately apparent from the exterior. Today, it houses a museum that you can visit.

• You can find details on current opening hours and ticket prices HERE.

Another landmark of the old town is St. Peter's Basilica, whose tower you can see from pretty much anywhere in the center. The renovated church serves as a venue for concerts and other religious events. For a small fee, you can take a look inside, or pay a bit extra to climb up to the observation deck at the top of the tower. Even just from the outside, the basilica is worth a visit, and you can also find a perhaps slightly creepy statue of the Town Musicians of Bremen here.

If you're not too tired after you arrive, you can take a walk through the city to the cathedral at Dome Square. The Riga Cathedral was historically the main episcopal church until 1561. It is the largest medieval church and one of the oldest religious buildings in Latvia and the entire Baltic region, and it's definitely worth seeing, at least from the outside. 

• There is an entrance fee, but you can also go up the tower or take a closer look at the organ. You need to book both of these activities in advance - you can find more information HERE.

Otherwise, you can head to your accommodation.

The first stop is the Riga Central Market - a marketplace located in former World War II hangars. You will find everything here from fruits and vegetables to cheeses, meat, and last but not least, plenty of stalls with ready-made traditional food. The market is very lively, even on weekdays, so I recommend visiting in the early hours. Each hangar collects a certain type of goods and they are all interconnected, so if you want to buy something specific, you just need to walk a little further, and signs will tell you what you can find in that hangar. Fruit and vegetable stalls are mostly located outside between the hangars.

One of the central parks is perfect for a slow stroll along the well-kept paths or for sitting in the shade. Various events are often held here, not just for kids, so there’s a good chance you’ll stumble upon one.

The dominant feature of the second central park is the Cathedral of the Nativity of Christ, an Orthodox cathedral built in the 19th century that looks like a mosque at first glance. The interior is beautifully decorated, and you can visit it for free.

The surrounding park belongs to the art university, and events are often held here too. You'll usually find notice boards with event schedules at the park entrances, so be sure to check them to see if something interesting is happening nearby.

An area you'll likely pass through and cross quite often while wandering around the city is the Riga Canal. You'll find not just fountains and plenty of benches to sit on, but also the option to take a boat ride along the canal to the Daugava River and back. The whole cruise takes about 50 minutes and offers a completely different view of the city than walking would. You'll find the dock at the lower part of the canal on the opposite bank from the Tejo café.

• Buy tickets in advance either on the River cruises website HERE or you might snag a discount from time to time HERE.

Your second day will feature a historical stop at the Latvian War Museum. Admission is free, or for a small fee, you can join a guided tour, which starts every hour on the hour.

The exhibits are beautifully put together and will take you through the history of Latvia in a unique way. The World War II exhibition, in particular, is worth taking your time with. 

The town is located right on the edge of the national park, so there's no shortage of beautiful views along the way. A direct train runs here and ends its journey right in Sigulda, so you don't have to worry about missing your stop. Buy your tickets at least a day in advance on the Vivi carrier's website. Then head to the main Riga station next to the Origo shopping center (the right side of the building when facing it), and then all that's left is to enjoy the scenery until you reach the station in Sigulda.

The main landmarks of Sigulda are the New and Old Castles, which you can reach after about a 20-minute walk. Originally a summer residence of the king built in the late 19th century, the New Castle became a refuge for a guild of writers and journalists after being looted during World War II; they took care of its preservation and repair, and after Latvia gained independence, the Latvian government took it over and renovated it to the form we see today. 

The castle allows tours; on the ground floor, you simply borrow an audio guide (no need for your own headphones) and then you are free to walk through all the rooms.

There are also several other buildings in the complex that are worth seeing at least from the outside, a few small shops with handmade souvenirs, and a small cafe where you can stop for refreshments after the tour.

If you cross the moat, you'll reach the old castle, an original 13th-century residence. Unlike the New Castle, admission here is paid—you'll pay before the bridge over the moat. You can walk through the extensive courtyard or climb the wooden stairs to the top of the front wall, where you'll get a lovely view of the New Castle and all of Sigulda.

Since Sigulda is located in a national park, it would be a shame to visit only the castle. Head back to the town and at the first roundabout (near the sitting statue), turn left onto the comfortable pedestrian/bike path. Continue straight from here until you reach the forest (if you're unsure where to go, Google Maps works great here, even for walking paths). From there, just follow the signs to Paradīzes kalns, which will lead you nice and flat all the way to the viewpoint.

From here, you can see a large part of the national park, the nearby Turaida Castle, and if you're in the mood and have the right clothing and gear, you can head out on one of the hiking loops that Sigulda offers.

To get to the airport, take the bus from the same stop you arrived at (Grēcinieku iela near the House of the Black Heads) - use the underpass to reach the island in the middle of the road where the buses and trams stop. You can buy your ticket in advance at a newsstand or again at the ticket machine at the stop. Get on bus 22 and don't forget to validate your ticket by tapping it on the reader. The route is a bit of a detour, so give yourself plenty of time. Airport security checks are usually quick and without queues, so there's no need to stress about it.