Paris
Restaurants
Riso
Bestia
Dyonisos Taverna
Cafés, Bars & Nightlife
Szimpla
Zsiráf
Mika Tivadar Kert
Activities
Get a buggy and cruise around Sziget-Island
Go to the roundabout a the beginning of the island and rent a buggy. Check out the different rental stations and get the vehicle you want. Some might be more expensive than others. However most of them are cheap. Drive around the island and have fun.
Go to a thermal Spa
The map shows three Spas. Spa 1 is rudas baths which is the only one I have visited but there is no reason to switch since it is great. Inside is very beautiful with the main hall having colored tiles in the ceiling. On the roof is a 360 degree pool (pictured) and there are many saunas and steam rooms. Get the ticket with full access (about 25 euros) and enjoy. Also make sure to check the website beforehand as some timeframes only men or women are allowed (most of the time both tho). The other spas are more famous however, yet also more touristy.
Stroll around Budapest Parc
Just walk around the parc and explore a bit. There are also places to eat or drink inside it.
Spots
The fishing bastion
Great hangout spot for the later afternoon. You have a nice view over the city. There are often many tourists here. If you fancy a more quite spot walk a bit more into the town and there is the Pavilon spot.
Top of the Citadella
The walk to the citadella may take you around 20-30 minutes and you may sweat a bit. But it is well worth it as at the top you get the best view over Budapest. And sometimes there are also places to get a strawberry beer or some langos open.
On top of Buda Castle
The walk through Buda Castle is very nice and at the end you also have a great view over the city. Like all the spots they are the most beautiful around sunset.
Pavilon
Just a quick walk from fishing bastion the Pavilon offers a view behind the hill of Buda. Very nice place to hang out and chill.