Tivoli, IMHO, is a great day trip and has a spectacular restaurant there. However, Borghese is a nice side trip. If you have not been to Rome before, do Borghese and see some other Rome sites that day.
We didn't visit Tivoli until our 5th (my 8th) trip after at least 30 nights there. We are planning to return this fall.
BTW,I can't believe the fountains are not working. While there may have been a day or two that they were "dry," I think the news would be out if it were more permanent.