I'm going to be staying in Liguria during most of May, but will be traveling back up to Nice where I am flying out. My last night is in Savona (wanted to see the Fortress and a Christopher Colombus artifact). I am looking for a resource to know if I can board a train to Nice in Savona and about how long it will take to get to Nice. Thanks for any insight and previous suggestions for Hotel Windsor in Nice (I made reservations with a garden view as recommended)! Ciao Tutti!

Yes, direct trains do run between Nice and Savona, taking roughly two hours and 15 mins.

Thank you. Do you know where I can purchase tickets online or can I just purchase those at the station in Savona. again...thanks!

There are direct trains for which you'll need to reserve seats, but this can be done at Savona - trains are very rarely fully booked more than a few days ahead.
There are also local trains to Ventimiglia (the last station in Italy), from where French local trains run frequently to Nice. These have no seat reservations so you just buy a ticket and get on the next train.
The schedules are on www.bahn.de.

I don't think you need to book in advance as I'm sure you'll find plenty of available seats at the station. Have fun!