Not really. You can go out along Tevere, but the difficult bit is getting over the Roman equivalent of the M25. You might be able to follow it and then pick up the Via Portuense. We're still talking tedious urban riding, but compared to the alternatives it's not too bad (trust me on this one).
I've not ridden the Via Aurelia into/out of Rome. You can check it on
Google Streetview (I'd strongly advise using it to check any route you're considering) it's a four-lane dual carriageway - not awful, awful, but not desperately attractive. So far as I know, bikes can use it, but best to check using Google Streetview (look for no-bikes signs at junctions where other roads join it).
Other possible options to think about: either follow minor roads to the Lago di Bracciano, or stay in Ostia/Fiumicino/Fregene and start there, or if it's a weekend, take the metro out from Piramide to Lido di Ostia. There are also trains - but you'd need to check the timetables to make sure you get one that is equipped to take bikes.
Some links that might be useful:
Comune di Roma (Rome City Council)
Map of the cycleways (piste ciclabili)