which budget FM Tuner

What fun! vintage tuners! You should have numerous options in great gear at the used $200 price point. ...And, if you don't like it -- hello audiogon and good-bye experiment.

I picked up a SUMO tuner last year, and it's quite the little tuner! Great sensitivity.  I also bought my kid a used Cambridge Audio tuner (much more recent). It sounds great, but probably isn't "vintage".

old Yamaha (like I have) or a Blaupunkt car radio with a power supply (!)

I had a Sumo Charlie for a short time a couple years ago, nice tuner.  I have a Creek CAS-3140 w/Din to RCA cable that is wonderful.  I've owned it for a good 6 years or more.  I've also owned some other nice tuners in the sub $200 range.  I prefer analog over digital tuners, let me see if I can find my old tuner post which lists the ones I've had, there are many good choices in this price range.  If you can get a Sansui TU-717, jump on it, but I don't think they are selling in the sub $200 range, are they???  Been out of the used Tuna market for a while as I am very happy with my Creek.

Here we go, from 1/14/14:

1. Harman Kardon 330C rec'r
2. Mitsubishi DA-R8 rec'r
3. McIntosh MR-71
4. Sansui TU-717
5. Pioneer TX-9800
6. Dyanco FM-3
7. Luxman T-110
8. Luxman T-400
9. McIntosh 1900 rec'r
10. Yamaha CT-810
11. Quad FM-4 (din outputs)
12. ADS T-2 - fun to use
13. NAD 4020A
14. Pioneer TX-500
15. B&K TS-108
16. Dyna FM-3
17. NEC T-710 - better than B&K 
18. Tandberg 2020 rec'r - nice
19. Creek CAS-3140 (din to rca) - neck and neck w/Tandberg

FAVORITES: 3,4,5,6, 12, 17-19

Additional tuners since this post:
1.  Pioneer TX-8500II
2.  Sumo Charlie

The fmtunerinfo.com site is a good place to start, not the end all in tuner sound, IMHO.

I don't know if you would find this tuner within your budget, but my favorite vintage tuner would be the Onkyo t-9090II. No it's not a Day Sequerra, but for the money it is still a great tuner & has great retro wood paneling. Another good option is the Yamaha TX-1000.