Chandpole is the best area to live in Udaipur, in my experience. There are a lot of hotels, cafes, and rental services there. and it isn't much far from the major attractions too. if you're on a budget, I suggest finding a good oyo in chandpole, and if you're willing to spend.. you can stay at the many many grand (and not so grand but still quite lavish) options!
If you talk about best place to stay then hotel lakepalace is dream of many but if you talk about location then stay close to udaisagar lake near city palace.