If you belong to a club, finding a tennis partner is probably not a huge issue. Even if you don't know anyone personally, you can ask the staff to assist with a match. Likewise, if you just want to paddle the ball around and work up a good sweat you can just take your racquet and a can of balls and go to the park. It's inevitable you'll strike up a game with someone sooner or later.
However, if your intent is to work on strokes, pick up a step or two and generally improve the structure of your game, you'll want to find an opponent who's willing to face you on a regular basis. Ideally, you'll want a player who is better than you.
Granted, you might succumb to a certain amount of frustration by having the daylights beat out of you every time you take the court, but those are the wages of learning. If you square off with someone beneath your level, you'll never learn anything. So, what's more important?
The ideal tennis partner should put you way back on your heels. Their serve should be faster or more tricky, their footwork should astound you and they way they attack the ball should summon the desire to put your racket in the closet and play checkers. After all, why put yourself through this humiliation? Because you're a tennis player, that's why! Maybe you're on the defensive today, but all that is going to change.
Pitting yourself against a superior player can only serve to improve your game. You have to get resourceful. Every player has a weak spot. Some disguise it very well but it's there nonetheless. During the course of play, you'll have to learn to identify your opponent's "Achilles heel." And even the masters have a vulnerable spot.
Some partners tend to be "pattern players." They set up their approach the same way every time. To gain the offense and establish the pace of the game in your favor, you have to adjust and counter your opponent with shots that disrupt his plans. Undoubtedly, your opponent will feel the heat and, assuming he has a plan 'B', will alter his game to combat yours.
Now, you're on your way to some exciting tennis brawls and you'll have yourself an exceptional partner. You have to keep in mind, though, that when you start beating the daylights out of them, it's time to find a new tennis partner.