I live in a wonderful studio in Center City. I really love my apartment, but it's small, obviously, and on several occasions recently, friends have come through town and asked to stay with me. I've told them the situation, and they've all said things like, "Oh, it's ok, I don't take up much space," or, "I don't mind being cramped for a night." They might not mind, but I do! How can I accommodate my friends without putting myself out?
Squeezing in a Studio
You should never be forced into having overnight guests who you didn't specifically invite to stay with you, so "no" should suffice on your end. Though it's totally understandable why you're "explaining the situation" to them, you're actually providing them with loopholes to find a reason that they should be able to stay with you after all. If the simple no really isn't enough, you could tell them that you (or your landlord, or your cat) have a policy of no overnight guests. For some reason the word "policy" often convinces people that the thing at hand is unchangeable.
Maybe there's a way that you can help them make alternate arrangements. Perhaps some local friends of yours have bigger apartments and would be willing to have guests, or maybe you know some people who are going to be out of town and have empty apartments while your visitors will be here. You can also say, "I'm sorry I can't help with sleeping arrangements, but I'd love to get together for a drink while you're in town." Then it's their responsibility to find a place to stay, but you're still being gracious. There also are (gasp) plenty of hotels in town, and some of them are even affordable.
The flip side is that if these are friends who are coming to town specifically in order to see you, you may need to be more helpful. Or, when you're making the arrangements about whether or not to have people visit you in your current city, this needs to be part of the initial discussion. Perhaps in these cases, you could make an exception and accept an overnight guest once in a while for one night at a time. Air mattresses aren't the worst thing in the world, and one night of being cramped to see a friend you really care about won't kill you. It may even bring back fond memories from your younger days and be kind of fun. Obviously, if it's never going to be fun for you under any circumstance, don't do it, but it could be worth looking at your own aversion in another light.
I can imagine that even if you're the most private, most guest-averse person out there, you might have one or two people in the world who you'd be comfortable having spend the night in your studio (sibling? best friend from childhood?), in which case, if they ever ask, feel free to say yes even if you've said no to everyone else. Your policy doesn't actually have to be immutable, but be prepared to explain the discrepancy if these people know each other. Also, none of this begins to take into account the potential presence of a significant other in life who might, sometimes, want to spend the night. I know that's not actually your question, but it's worth examining for yourself whether your studio living is a way to keep people at a distance. If it's really just a price thing, then enjoy your personal space and and enjoy your guests from whatever distance makes you happiest.