Not a lowly battery operated radio, but the Kaito KA600 is a pretty decent radio. Good FM/AM/NOAA reception and it covers a lot of short wave (2.3KHz-23 KHz).

Power options include:
1. Rechargeable battery pack,
2. Standard AA batteries (I use NiMH rechargeable batteries),
3. Solar (power radio and recharge battery pack),
4. Hand crank,
5. USB,
6. 120 Hz AC

Mine doesn't get much use, too many radios

Not affiliated.