The Hungarian currency is the forint: HUF, on average EUR/HUF rate = 330, USD/HUF rate = 305, GBP/HUF rate = 380 (September 2019).
Budapest in early June is typically warm to hot (usually 25-30 degrees Celsius).
Coffee and cake
Close to the conference site is Matinée (Benczúr u. 2), which serves the most amazing coffees and cakes (although those sell out in the early afternoon). For very elegant coffee houses you could try the New York Palace Cafe (Erzsébet krt. 9-11), or Café Gerbeaud (Vörösmarty tér 7-8).
Plenty of restaurants can be found all over town. Many are located along Kazinczy utca, Liszt Ferenc tér and Ráday utca, with a lot of tourists buzzing around. Király utca is close to the conference hotel and has many nice restaurants. The local prices are lower than in most European countries, allowing you to have nice meals for not much money. A few nice places close by are:
Paprika, Dózsa György út 72 (Hungarian, really good)
Király utca 100, (Hungarian restaurant, very good)
Pinsa, Király u. 69 (authentic Italian pizza)
Bao Nam Phở, Király u. 71-73 (best pho in town, mainly take-away)
Biang Bisztró, Teréz krt. 20 (authentic Chinese street food, very nice)
Borbíróság, Csarnok tér 5 (Hungarian, very nice wine-food combinations)
Vegetarian or vegan:
Kozmosz, Hunyadi ter 11 (small place, but good menu and cheap)
Napfenyes, Ferenciek tere 2 (quite elegant and with a large menu, good food!)
for more options, you may check on happycow.
Drop, Hajós utca 27 (very nice)
Bars and Pubs
Hopaholic, Akácfa u. 38, large selection of beers
Kadarka, Kiraly utca 42, is a nice wine bar where you can try Hungarian white and red wines.
There are beautiful museums in town. Besides the famous ones usually recommended in touristic information, we would definitely suggest the Magyar Természettudományi Múzeum. They also have a great collection of meteorites.
Some suggestions to spend an extra day in Budapest:
Budapest is called the city of baths: http://www.spasbudapest.com/. The most famous Széchenyi baths are located in the City Park, very close to the hotel (also along the M1).