Hi Tinker. We actually stayed in a one bedroom apartment (with two fantastic sofa's in the living room which our kids slept on). I would certainly recommend you stay somewhere not too close to St Marks / The Rialto etc as it is SO crowded and the whole place is just so beautiful that you don't need to be in the touristy bit. Our flat was £400 a week and was situated around a 30 min walk from St Mark's but just metres from a vaporetto stop which went to the Lido, Rialto, Murano and St Mark's. It also had a range of delish neighbourhood food shops nearby which meant we only ate out once (a blessing as the food in Venice is often expensive and not very good).
We went to the Lido one afternoon. It is a quick trip and the boats are frequent. However, it is pretty much deserted at this time of year with a lot if not most hotels and shops closed. It was also a lot colder than Venice itself. Have you looked on LastMinute.com as they seem to have some reasonable deals on 3 star hotels?. I would try and avoid the Train Station area to stay in but don't be afraid to go for somewhere in a more out of the way part of the city. There are no crowds at all except in the main areas.
As for eating, as with hotels the further away from St Marks the better and don't go with high expectations.
I can't tell you what a wonderful time we had. We went slightly mad and ended up standing on the deck of a water taxi down the Grand Canal at midnight on New Year's Eve (with baby daughter snuggling up to me and looking dreamily at the scenery and toddler son screaming manically that we had to close the doors and come inside NOW) and the next day also went on a gondola (which at £50 cost considerably more than our outward flights!!).
And be prepared for Treviso airport offering very little in the way of shops/ food etc but it is only 25 kilometres from Venice so is a painless and quick bus trip. When you get off the Ryanair bus, make sure you look for the Vaporetto signs and don't be misled by the gentlemen ushering you to the "Water Bus" which is a private thing charging around EUR10 a head rather than EUR2.
I really hope you enjoy it.