We stayed at Michele's Monti apartment for a week and we throughly enjoyed it.
When standing outside the apartment the Colosseum is in full view. You literally cross the road, walk down a few steps and you are there.
Right next door to the left are two restaurants, further down the hill to the left and across the road is an area called Via Giovanni. It's a very friendly gay area with very good, cheap restaurants and amazing eats! I HAVE to recommend Cremeria Don Pepe this is the best ice cream you will find in Rome, pure bliss so don't miss it!
If you were to turn right at the apartment and follow the hill you will come to even more restaurants, souvenir shops, mini-markets etc.
I recommend taking a taxi to Elite to do food shopping as the prices there are a fraction of the prices locally and much more choice! The apartment has ample kitchen facilities, bring a travel kettle if you want a quick cuppa! There is no toaster but there is a pretty good cooker with a grill for toast.
We had an issue with the boiler and hot water while we stayed but Michele was very on the ball and came to the apartment with a plumber at 10am the next morning and fixed it, then we had an electricity problem but it was sorted just as quickly. Michele is a very good host and I can't thank him enough for our experience in Rome.
Just a bit of advice for any new tourist to Rome (...we learnt the hard way!) don't get cornered by the Gladiators for pictures, they'll charge you €5 for the privilege! Totally walk past the "selfie-selfie" guys, they'll think your a local. Don't go on the guided tours unless you have time to kill, it's totally not worth it!
If you want to go shopping head for Via Del Corso and have a blast, so many shops there you could spend all day at Via Del Corso and never see all the shops! You can walk from one side of Rome to the other, but getting on an open tour bus made life so much easier for us!
As other people have said the apartment is a basement apartment and does have a slight damp smell but nothing you don't get used to. The sofa bed is very comfortable and the Wi-Fi where it isn't super fast it is super reliable.
I can recommend this apartment to anyone wishing to stay in the heart of Rome!