Regarding places to stay, I can tell you that we stayed at the Marriott hotels closest to the city center in Prague, Vienna, and Budapest, partly because we were able to use Rewards Points to get the rooms for free, partly because the locations are excellent for exploring the main attractions, but also because we find the accommodations reliably comfortable for spoiled Americans and my wife loves to end a busy day of adventure with the complimentary wine and desserts in the Executive Lounge. :rolleyes: Aside from those hotels, however, I would highly recommend the Hilton Budapest, which is ideally situated on Castle Hill above the Danube, adjacent to Matthias Church and the Fisherman's Bastion; our friends who went a year after us stayed there and thoroughly enjoyed it.
I can't speak for any restaurants in Budapest -- though let me second the suggestion of another poster to visit the Central Market Hall near the east end of the Liberty Bridge, and bring an appetite. But for Prague, I would reiterate my recommendations of Hergetova Cihelna [
http://cihelna.com/en/] (on the west bank of the Vltava River, just north of the Charles Bridge -- a perfect setting for a splendid dinner at sunset) and the Cafe Imperial [
https://www.cafeimperial.cz/en/homepage/] (which offers fabulous decor and ambience of local character along with fine cuisine at reasonable prices). In Vienna, we enjoyed dining at one small contemporary restaurant, Paul Restaurant Brasserie [
https://www.paul.wien/] (located on Johannesgasse just one block off the Ring from the southwest corner of Stadtpark near the Kursalon), and at one of the larger traditional Vienna eateries featuring local cuisine, Plachutta Wollzeile [
https://www.plachutta-wollzeile.at/en] (located on Wollzeile just one block off the Ring from the northwest corner of Stadtpark).
Wherever you choose to stay, and wherever you choose to dine, I'm confident that you will have a delightful experience! Be sure to take lots of photos.