For nothing too strenuous I would look at yoga, pilates or something like callanetics (lots of small movements, good workout, not high impact).
For bingo wings - hold a weight in both hands above head, arms against ears. Keeping elbows still, lower weight to behind head and return to start position. Important to keep upper arms and elbows still. When I say weight, I don't mean anything really heavy! Just a can of beans, empty 500 ml water bottle (can then fill when you get stronger) etc. Just something that offers a bit of resistance.
Also a good idea to do bicep curls too. Again keeping upper arm and elbow still, curl arm upwards, palm facing upward holding weight.
Can also do tricep dips
http://www.fitsugar.com/1055754 not sure about the web site, but they have a picture!
For starters you can do these just on the floor. Instead of lowering yourself down, place your hands on the floor and lean back slightly, then return to the upright position whilst still leaning back to engage your tricep muscles.
You can also do press-ups, but against a wall. This way you're not applying a lot of weight and not risking your back. Just do pressups as you would normally, but standing, against the wall. Just lean forward slightly so you actually have to push away from the wall. Hope that description made sense!
Swimming would also be good for the resistance the water offers and the low impact, but I hate hot, chloriney pools.