We just returned from our first trip to Budapest. It’s a lovely city - reminded us a lot of Paris but…a bit grittier? Which I liked - I prefer big European capitals where you feel like you’re actually part of the hustle and bustle of the everyday life for people who are living there. And, like Paris, Budapest is quite grand. We stayed at the Alice Hotel, which I believe I read about in this forum. Look up Mr. E - he has a ton of very useful recommendations, particularly for accommodations and restaurants. The hotel was a lovely business hotel on a very nice stretch of Andrassy Ut, convenient to City Park and Széchenyi Baths, and we liked taking the historic M1 metro line. That said, when we went across the river to explore Buda, I really liked the vibe on that side of the Danube. Personally, I would like to stay there if we ever go back. It was more quaint and a little sleepy, so honestly, I guess it just depends on what type of atmosphere you are going for. Staying on the Pest side is likely more convenient, though it’s not like it’s hard to get around via public transportation or Bolt if walking distances are too far.
We had one of the best meals of our lives at Parisi Passage restaurant. Amazing service, as well.
Don’t miss the Dohany Street Synagogue or Terror Haza Museum. Obviously the baths are a must and worth a day or two (we did Széchenyi and Gellert). We also really enjoyed the Hospital in the Rock tour. No matter where you stay, make sure you are on the Buda side at and after sunset, so that you can fully appreciate the Parliament all lit up. In my opinion, it was the single greatest sightseeing experience in Budapest to just sit on the banks of the Danube and look at that parliament building all aglow. Absolutely magical!