I recently travelled to Venice after celebrating New Years in Rome and it was quite a pleasant experience.
I was also on a budget but i made it through the stay without any thoughts of retrieving my credit card. Venice is actually pretty affordable, thats if you dont splurge on the souveniers of course.
If you're on a budget too, here are some tips that might come in handy...
We'll start off with the accomodation. To be in Venice, you don't actually need to stay in Venice, especially in the San Marco Square because you'll end up paying about 250 euros a night in that area. Opt for the suburbs where you can easily find a room for 30 euros a night and it only takes a 5 minutes bus trip to Piazza Roma, where you'll need to be on foot for 15 minutes before you arrive at San Marco. When you're on foot, you'll come across the Rialto market where they have a maze of stalls selling all sorts of souveniers, including the carnival masks
I stayed in Venice Rooms off via Casona and i fully recommend that place to anyone travelling to venice on a budget because you have a bus stop 15 steps away from your door step and a supermarket just across the road and you're only paying 36 euros a night for a private room. Plus, it includes breakfast and allows you to cook. And if you cook in Venice, you'll prolly just need 5 euros to buy yourself 3 meals that includes pasta, bacon and red wine. Yes, stuff in the supermarket is amazingly cheap. 39 cents for a bottle of red wine - how does that sound? In the morning, take bus number 12 or 24 and that takes you straight to Piazza Roma for just 1 euro
When you arrive at Piazza Roma, you'll start to see stalls selling souveniers. Kill the temptation and keep heading towards Rialto or San Marco because the deeper you go, the cheaper the stuffs go. Its the opposite for food tho where the deeper you go, the more expensive it gets. Near Piazza Roma, you can buy focaccias or slices of pizzas for anywhere between 1.50 - 2.50 euros. At San Marco, it can go up to 6 euros.
When you've in Venice, drink plenty of wine and beer because you'll never find a shop that sells Coke cheaper than wine or beer. A can of coke is usually 2 euros and its only 88 cents to fill up a 1 litre bottle with wine
Take note that the gondolas will cost you 80 euros per head per hour so if you're on a budget, go on foot because you can literally get anywhere on foot. And trust me, you see far more stuff if you go on foot - especially the alleys in Venice
OK, let's come back to the souveniers because very unlikely, you'll leave Venice without buying some souveniers. Venice is known for their carnival masks & murano glass. My best advise is get to Rialto before you start shopping. There, theres not much difference in prices amongst the maze of stalls there. When you get a mask, get it off the street stalls because they sell for like 200 euros per mask in the boutiques. At the stalls, it ranges from 10 - 30 euros, depending on the architecture and design.
In terms of places to go, Venice is actually not that big and you can pretty much cover it in 1 full day. An easy guide will be to walk from Piazza Roma to San Marco and you'll pass the Rialto and thats pretty much the must go places. Spend a lil more time at San Marco, especially in front of the Basilica where you can buy bread crumbs for 1 euro a packet and start feeding the pigeons. After that, head towards the sea shore and snap many pictures there. You can also opt to take a gondola there to get to the island