Yes, Uranus is currently visible and will be for quite some time, not just tonight. However, it's at magnitude 5.7 which is close to the limiting magnitude the human eye can see unaided, which is around 6, so it's not that easy to see. If it's clear tonight (and for the next few nights) then the moon won't be a hindrance.
It's a tough observation, even for seasoned observers. The way I would try and find it is waiting until midnight when it's almost directly overhead. Then, try and locate Cassiopeia (the big "W"). If you assume the W is made of two Vs, then the larger of the two points toward the Andromeda galaxy (visible to the naked eye, will appear as a faint fuzzy ball of light). Then, go about the same distance again, and that's the current location of Uranus. If you can identify Pisces, then it will help (this chart may help):
http://www.nakedeyeplanets.com/uranus.htm#finderchart
Some may be wondering why Uranus seems to be reversing its direction, but this is normal, it's called retrograde motion. It happens when the Earth "overtakes" one of the outer planets in their orbits. As it overtakes, the outer planet appears to reverse direction, only to reverse it again a while later. Astrologers will be able to explain all the dire effects this will have on us...