Budapest visit Dec 29-Jan 2

Hi IN members in Budapest,
I'll be visiting Budapest Dec 29-Jan 2 with a friend and wondered if anyone has suggestions on places to stay. I was thinking of an apartment. What areas are nice to stay in?
Are there any parties or events for New year's eve that you can recommend?
I've been reading up on places to see (restaurants, bars, sights, etc) but any suggestions are welcome.
This is what I have so far - some more restaurant suggestions would be nice.
Sights
Gellért Hill
The Castle, Citadella
The Liszt Academy of Music
Eiffel square (ice rink)
Műjégpálya (City Park, ice skating)
Városliget: Heros’ square and Kazinczy street
Kopaszi-gát at Rákóczi Bridge
8th District – walk around here as it
Hungarian Parliament
Szabadság tér
Andrássy Avenue is Budapest’s Champs-Élysées
The Danube Fountain on Kálvin Square in Pest
Heroes Square
Fisherman's Bastion - The Statue of St. István
Buda Castle, Sandor Palace, Matthias Church
Buda Castle Hill Funicular
Danube Promenade
Liberty Bridge
Elizabeth Bridge
Chain Bridge
Women with Umbrellas, Óbuda at No.7 Laktanya utca (then go to Imre Varga Museum)

Restaurants
Liszt Ferenc square and Ráday street- restaurant jungle
Padron (Spanish) located in Horányszky utca

Bars/pubs
Tip Top Bár (Pub) on the Egyetem square, it’s on the top with a wonderful view.
At Bazilika square: Divino wine bar (nice wines, lots of people)
Deak square (Deak Ter): Nice bars and cafes; Acvarium (night club), Fröccsterasz (closed in winter)

Nightlife
Uri Muri on the Andrássy Avenue, Ötkert, Szimpla kert, what is a must for foreigners.
At Corvintető the view is wonderful – might be closed
Rákóczi Bridge A38 (it’s a ship). Király street, Deák square and Kazinczy street are always busy, you will never be bored around these places.
Mika, Ellátó, Kőleves, Protected content nightlife at any of these places.

Spa/Baths
Lukács Bath
Széchenyi Bath
Veli Bej Bath