The biggest complaint I hear from fellow travelers is that it often feels lonely traveling on the road. Since you're there for just a few days it's very hard to meet new people using the methods you often use at home. Try some of these methods and I'm sure you'll make some great friends, lickety-split!
Meetup is the first place I go to meet people. Basically it's a site where people post events specifically tailored for meeting people. The membership is HUGE and they post meetings for all kinds of different events for all kinds of different people. This is by far the least intimidating way to meet new people because everyone there is there to do just that. Every time I'm in a new town it's the first thing I check and I always end up finding something awesome to do!
Why meet people when you can just sleep on their couch? I've said it before and I'll say it again: couchsurfing is AMAZING! No matter how shy you are, if you try this site you'll definitely make friends with your host or the people you host. Also be sure to check out the group page for the city that you're in. People are always posting random meetings and events specifically designed for meeting new people and don't forget to announce your arrival on there too! Somebody will surely contact you to meet somewhere.
A little sketchy and I must say I haven't tried it myself but feel free to post an ad on craigslist announcing your arrival. Somebody interesting may just write you back with an opportunity to make some friends. If that's too creepy for you then at least check the community section for any event announcements that look interesting to you.
Volunteer For a Day
Many organizations love getting volunteers, even if it's just for a day or a few hours. If you participate in some kind of volunteer program at home then you should try looking for the same program in the area you're traveling in. You'll be the center of attention as you tell people you spent one of your vacation days helping out and people will love hearing how differently things work in a completely different location.
Just randomly go up to someone and talk to them. Rinse and repeat. It's super scary and it takes a lot of confidence but sometimes the best way to meet someone new is simply to go up to them and introduce yourself. I've done this a ton of times and it always ends up well. I've only gotten turned down a few times and it's never as bad as your imagination lets on. Just tell yourself that the best case scenario is that you make some new friends and have an amazing day with them and the worst case scenario is that you just have to try again.
Take Buses and Trains not Cars and Planes
Even though it's significantly longer and a lot less comfortable (and in the US it's not even cheaper!), taking a bus or a train to your destination is a much better way to meet people who are also heading to the same destination. You'll have the time to get to know each other and you'll both be significantly bored enough to want to talk to a stranger.
Whether you're moving to a new town or just visiting, meeting new people can be incredibly scary but also wonderfully rewarding. Even with an increasing world population, it seems like it's even harder to connect with people. If you try hard enough and look for the resources, though, I guarantee that you'll be rewarded with some amazing friendships.