If your trip is long enough, you will have to do laundry (or not, depending on how much basic personal hygiene matters to you). Packing light and carrying your luggage on trumps bringing enough clothes to avoid doing laundry so here are your options: do it yourself in your hotel room (shhh-hotels frown upon this), go to a laundromat and do it yourself, or have it done for you by the hotel (ooh-la-la) or at a cleaners.
The first option is the least convenient but most economical. Bring your laundry soap in a carry-on friendly 3-oz container and do your washing at least a day or two (depending on climate) before you have to pack up your bag again to allow for your clothes to dry sufficiently (remember, no spin cycle). The second option will cost you a little bit of money, but a lot of your time. Going to a laundromat would be the best option if you are in a place for an extended period of time, but on a 2 week vacation, the 2-hour commitment can be a deal breaker. Option three is the easiest because you do nothing, but it will cost you. Just like eating at a hotel, doing your laundry there is spendy because of the convenience, so seek out a cleaners in the neighborhood. Often you will find that they will do a load of your laundry for $10-$20. I know this sounds expensive, but the alternative is bringing a bag you would have to check (remember those checked baggage fees!) or spending a couple of valuable vacation hours in your room or a laundromat. Take your bag of dirty clothes there in the morning on your way out for your day’s adventures, and pick it up on the way back. For a drop in the bucket (compared to your overall vacation budget), you have suitcase full of fresh clean clothes for the second act of your trip.
Know Before You Go
Bring plastic bags to put your dirty clothes in. If your trip is long enough where the rules of hygiene would be broken (or even stretched a bit too far) if you did not wash your clothes, plan on doing laundry. If you are a DIY-er, remember the detergent. If you prefer to use a laundromat or cleaners, use Google to find ones in the neighborhood of your hotel or ask the friendly (hopefully) staff when you get there.
Long trip+packing light+carry on luggage=laundry