So, as everyone else as said here, it's very important to listen to your body.

Having said that, anything you do that causes you to expend energy in such a way that it takes away from your body's resources to fight the infection, will lead to an extended healing time. If you're young and healthy, you may have a ton of physiological resources to draw from and it might not be an issue. So if you feel great and you really feel like you need to exercise, then go to it.

Also, as everyone else has said, hydration is extremely important with UTIs. So if you choose to exercise you have to be even more paranoid about your fluid intake. Drink tons!!!! Flushing your bladder frequently helps to carry away the bacteria that causes the UTI in the first place.

Finally, you only lose about 1% of your cardiovascular fitness by not exercising at all for 1 week. After that it starts to drop rapidly. I've had too many UTIs to count and my philosophy is that I want my body putting all of it's energy into fighting off the bug, so I tend to rest for at least a couple of days knowing that the rest is not really going to cause any significant harm to my fitness and could speed up my recovery.

Of course your mileage may vary.