Cute little radio...
 

It works but only has AM and no antenna, I guess it was designed for city life.

Its AM only and there's not a ferrite bar antenna inside? Weird.

...But it IS a "Superheterodyne"...Whoa !! (grin)

But it gets real fuzzy-looking when you put it in the case. Wonder why?

Not tuned in good? :D J/K FFR. It's a cute little radio.

It is a 2R-21 made in 1965. That accounts for the fuzziness.

http://www.transistor.org/collection/sony/sony2.html

Is there any way to improve the reception, anything I can clean or whatever?

Well, the first thing to do is to verify whether it has an internal antenna or not. If it has a ferrite bar antenna and the bar is broken, it will need to be replaced. Reception with a broken antenna will be very poor. If the antenna and it's wiring is in good condition, then all it should need is simple alignment of the IF stages. Pretty easy on AM radios if you know how. Check for battery corrosion on the board too. Clean and resolder where any damage may have occured.

I think it does - copper wire wound around a bar of some material, positioned right above the tuning mechanism? Thanks, cg

Yep..that's the ferrite bar antenna. It's possible some of the caps have dried out and need to be replaced. (Forgot to mention that.) Then tweak the alignment. Should be a fairly easy and inexpensive task to perform.