Vatican city on our own

No. Was it a tour company or travel agent selling guide service that suggested this to you? Who would rush you????

@ORDtraveler, it was a friend of a friend. I didn't quite believe it. Thanks for the confirmation.

On the contrary, even the official tours will not show you everything (!) in the vast art museums section. You have to go back and visit on your own if you want to cover more of it. However, there are sections like the gardens that are only open by house tours. Another issue that comes up often here is whether you can get into St. Peter's faster by having a guide in the Sistine Chapel - with rights to use a special exit. No current comment from me.

There is food available inside, with fresh air and later re-entry to the museums, which can be helpful in a plan like yours. It is important to understand that all parts of the Vatican complex are fiendishly crowded, despite advance ticket sale. Note that Vatican City may not be the precise term for your OP "destination" - not as a correction, but for use in further research.

Vatican City comprises lots of things in a compact space - residences, the Basilica, the Museums, and other facilities.

I have never been rushed visiting St Peter's. Sometimes the queue to clear security can be quite long, but relatively fast (good because it is out in the sun) but once inside all the time I want.

The Museums again can have long, slow queues for people buying tickets on the day, and then the Museums security line.

The Museums can be (almost always are) very crowded and if you allow yourself to be pulled along by the crowd you can feel that you don't have enough time. The truth is that once you are in you can be there as long as you like until closing time, so all you have to do is step to the side, go into the side rooms full of special stuff that the vast hordes just whizz by - many rooms you can have nearly to yourself. You don't get that on a guided tour. You will be guided, and at the speed of the guide not your speed.

As said above, go and get some air at the pineapple, have some food, and plunge back in...

Do buy your museum tickets in advance. The lines can be very long depending on your date.

Edit - Above advice is great re the museums. I remember relaxing in the Etruscan collections. Not much interest from many visitors - we found much fascinating!