Given that there are very few high-quality FM stations left, and the broadcast quality of AM is a moot point, don't spend much on a tuner. There are some very good, used Japanese-made tuners from the late 1980's and early 1990's that are inexpensive and offer very good performance. One of the best tuners I ever owned was a NEC T6-E (which cost about $250 new), and I still regret selling it (I think I got $75 for it). My current tuner, which I use exactly as you propose to do, is a Proton 440, and it filled the bill very nicely for me.
The following tuners are currently listed here on Audiogon for less than $200 and -- assuming they are in good working condition -- should do nicely to meet your needs:
1. Sansui T-7 ($50): http://cls.audiogon.com/cgi-bin/cls.pl?misctunr&1154525010
2. Rotel RT-935AX ($95): http://cls.audiogon.com/cgi-bin/cls.pl?misctunr&1154390780
3. Sansui TU-S9 ($195): http://cls.audiogon.com/cgi-bin/cls.pl?misctunr&1154028038
4. Harmon Kardon TU 912 ($80): http://cls.audiogon.com/cgi-bin/cls.pl?misctunr&1153493497
5. Adcom GFT-555 Mk2 ($125): http://cls.audiogon.com/cgi-bin/cls.pl?misctunr&1153171351
6. Luxman T-215L ($75): http://cls.audiogon.com/cgi-bin/cls.pl?misctunr&1152724357
7. Cambridge Audio T-500 ($130): http://cls.audiogon.com/cgi-bin/cls.pl?misctunr&1152724357
There are two additional costs you might have:
1. replacement of the aging electrolytic capacitors (15 years is about the max lifespan);
2. a good outdoor antenna, which you will probably need if you live in an area that has lots of multipath distortion problems (say, downtown NYC), or is a long way from the broadcast antenna.