When I travel, I often just use the laundry service that most hotels offer. Yes, I know, it can be expensive, but after spending thousands of dollars on a trip, I don't worry about spending another $20 or $30. They usually do a great job and return the items by the end of the day. They've been known to get small stains out that I've failed to get out over many washings!
I do do some laundry in the sink, but only small, quick-dry items.
If you're renting an apartment, then finding one with laundry facilities included would be the way to go.