Rome Park Hotel: If you like you can spend 10EUR for hotel provided shuttle bus directly to the city center - every 2 hours from morning till evening. But if you like to spend less the is a nice option - bus stop just outside the hotel area - it costs 1 EUR to get in 5 mins. by bus to train station and then every 10-20 minutes depart trains to city center (it takes around 20-30) minutes to get close to Colosseum. So the whole journey takes 30-60 minutes depending on traffic conditions.
Courtyard Central Park Hotel:
is vey well located - just 5 mins. to train station Gemelli and then every 10-20 minutes you got train.
you can get out:
4 stops later: metro line A,
5 stops later Vatican
6-7 stops - don't remember exactly - and a short walk to - Pyramid plus Colosseum
There's a train station just up behind the hotel (Courtyard Rome Central Park) For one euro, you can travel into Rome. I believe you can use it also on the Metro within a certain time, I'm not sure. However, the trains run regularly and it is under 10 minutes' walk from the hotel. Obviously, it is more convenient to stay downtown, but it isn't all that much trouble to get downtown from there.
Just to update this thread with current information, I emailed the Courtyard Rome Central Park front desk yesterday, inquiring about hotel shuttle service and received a kind and prompt reply, which contained a shuttle map and schedule. The shuttle goes to/from the hotel to the Vatican only. From the Vatican you can either walk to points of interest, or catch the metro. You can also take the regional train to/from the hotel into central Rome, the FM3 line towards Gemelli, but the problem with both the shuttle service and the train service is that they stop running at 9-9:30pm, which is just too early. The shuttle is 3€ each way. The train I think is a bit cheaper. I have attached the shuttle schedule.