for less than $100, if you don't mind buying used, I would suggest a
gently used Sony ICF-SW7600G. Be careful, Sony has made a variety of
radios in the 7600 line (some very good, some not so good). The newest
in the line is the 7600GS, but that'll set you back around $160, if
memory serves. It's predecessor, the 7600G, had fewer memories but has
nice features like single sideband reception and sync detection
(advantages of sync detection is a matter of some debate; some think it
helps, some don't). I had one for several years before trading up to a
ICF-2010 (on which I can say the sync detection *definitely* helps) and
haven't looked back. But for $100 the 7600G is a lot of radio.

I also see the Sangean ATS-909 (and it's rebranded brother, the Radio
Shack DX-398) selling for $50 to $150 used. If you are into FM, it has
RDS built in. It has continuous SW coverage like the 7600G. I can't
attest to the dx qualities of this radio though.