Good FM tuner for around $1K

Magnum Dynalab makes several models of FM Analog Tuners that work very well. Personally, I have the MD-106T but there are several to choose from new or used. I believe they all use tubes, but I could be wrong.

The Mac MR 73, 74, 77, and 78 are all available for under $1000 used. Their RF capabilities are unmatched. Audio Classics often has all of them in stock.

There is a Magnum Dynalab MD-90 listed here for $600. I have that tuner and it is outstanding. The list price for that model is $1400. Here ya go!
https://www.audioadvisor.com/prodinfo.asp?number=MDMD90

You will have to buy used. Not many making tuners anymore. McIntosh and Magnum are the few that are still around, and their tuners go for a lot more than your budget!

You should be able to pick up a really nice used tuner for $300-$500. 

The fmtunerinfo web site has (subjective) rankings of what the best tuners are and information about typical sale prices.

While the tuner itself is important, even more important is getting a good signal to it.  Use some of your budget on a good roof mounted antenna. 

I have an Onkyo T9090 II that I enjoy every day and with a good signal it comes close to CD in terms of sound quality.  I paid $200 for it.