The East Village is jammed with restaurants, bars and boutiques. Far too many to list.
The cheapest hotel probably is the The GEM Hotel-SoHo (which is on Houston Street and used to be a HoJo but is now run by Choice Hotels (
The GEM Hotel). It was built in the last five years and is basic but clean. The East Village proper doesn't have many hotels but nearby neighborhoods do (Lower East Side, SoHo, Union Square, West Village).
For something more high-end you could try the Hotel on Rivington (
Hotel on Rivington). Very hip and trendy.
Hotel prices are really in flux right now. Formerly expensive places are offering great deals. It pays to shop around. The price difference between a high-end and mid-range room is not what it used to be. Use Quikbook (
Quikbook Hotels: Discount Hotel Reservations - New York and Other Cities). It allows you to make a reservation without prepaying; that way you can find the best deal.
Cab fares are based on distance so it depends on where you want to go. I live in the East Village and it's less than $10 to Chelsea. About $12 to $15 to Times Square.