Can I cook hamburgers in the microwave oven?
In short, kind of, but only with the proper accessories/equipment.  You'll never match a grill or griddle but you can get surprisingly close.

As was mentioned in other answers, what you're going to lose most is the sear.

I was given a Corningware Microwave Browning Dish a while back and found that it actually works pretty well when you're stuck with only a microwave.  They were apparently popular when microwaves were new and exciting, but people didn't know how to use them well and they faded into oblivion.  I've seen them on sale on eBay so you might be able to find a good price there if you're going to be stuck in the hostel for a while.

The basic idea is, there's a special kind of microwave-safe metal inside the base of the casserole.  You heat this with nothing on it for 3 minutes to get it nice and hot.  When you drop the patty on, it immediately sizzles.  You use the microwave function to heat the inside, while the hot surface sears the outside.  Although you're likely not going to get a perfect burger, you do get a real nice Maillard reaction on the outside of both sides (assuming you flip halfway) and if you play with the cooking time and power (to reduce that rubbery texture from overcooking), you can get something that's (in my opinion) a good 75%-quality burger compared to a griddle or grill.  I actually burned pork chops on it once, that's how hot the surface gets.

As a bonus, similar to a nice Boos block, there is a gutter around the outside and the plate is slightly concave, so the juices run off into the reservoir and the burger won't sit in fat during the cooking.

After reading the other answers (ElendilTheTall's specifically), I would think if you combined the steaming method to cook the burgers, with the microwave browning dish to sear, you could probably get a really good result.  If the burgers were fully cooked via steaming you could probably heat the dish and sear the burgers without even turning the microwave on (except to heat the casserole initially).

I believe Alton Brown did an episode where he talked about a specific type of brick that you can find at most hardware stores which is microwave-safe for the same searing purpose, but I can't find that info right now.