If purchase price, and cost of insurance/registration/etc don't matter, then all you're looking for are vehicles that won't depreciate much. Those break down into two categories:
1) vehicles at the bottom of their depreciation curves - typically older, higher miles. They'll have very low purchase price, and will be cheap to register/insure. (you seem reluctant to go this route for a few reasons)
2) new vehicles that don't depreciate much - you can just google this. You'll get lots of trucks and Jeep Wranglers and things that will make terrible city vehicles but there will be other options too. Many of those other options (camrys, etc) would also fall into ideal vehicles from the first category too, where they have strong reliability and a low buy-in. People know this and that's the reason for the slowed depreciation.
A Tesla might be an interesting option, especially if there would be any kind of state funded tax credit for buying new. But do you have a place to charge it regularly? Is your valet reliable enough to do that frequently? Or could you charge while at work? Insurance costs for Teslas are all over the place, which makes that hard to predict. And their network of service stations is sparse in most of the country, so if anything were to go wrong you might experience more downtime than other more traditional models. They also have some track record (minimal as far as I know) of removing features paid for by the original owner when ownership changes, and that might impact resale value.
