Being a former record engineer, my experience has been that places generally charge between $80-120/hr, depending on a number of things (how expensive is the equipment you're actually using, the experience of the engineer, etc.). If they charge more than $120/hr, I'd go somewhere else.
If you want the best recording you can, I'd split the recording over a few days, so you don't get tired. Maybe 2-3 hours a day for a few days? You don't get a better rate if you have multiple hours at a recording studio. Remember, they deal with rock and jazz bands all the time who pay for like 14/hr days for weeks at a time to get their sound just right. We pianists are small-time jobs for them.
Most uni's offer a recording, I would think. The uni's I have been at have offered a "free" recording. I say free because the recording service was included in the price I paid for the hall reservation. If you want a better recording, hire a professional to record your recitals. They'll have better mics (and better mic placement as well) and will give you a better product than the run-of-the-mill product you'll get from the amatuer students working on your CD at a uni.