As I read the OP's question they are wanting to attend a mass on a certain date (irrespective of whether the Pope is celebrating that day) but were inquiring whether there would be the added 'benefit' (or whatever other word you want to use) of having the Pope celebrating.
Whether or not the Pope was in good health that appears to be a piece of string. Like in any Cathedral round the world (eg St Paul's Cathedral or Westminster Roman Catholic Cathedral in London) whether or not the Bishop of the Diocese is celebrating on a particular day is not announced more than a few weeks in advance. Reading the website that appears to be the case at St Peter's as well. Reading the website it seems that there isn't a way of getting the free tickets online- you turn up, write in, email or call them, so does take a degree of effort and commitment.
There is no "best:" chapel. A mass is a mass.
I at least understand what this means. Yes mass is mass, and it doesn't matter where it is held. But even in my little local Cathedral (Carlisle) there are different Chapels- some of which are more interesting than others- some are only open for services, not the casual visitor, so there would be an added benefit of Mass or Office in one of the side chapels as compared to in the Quire or the rather open Regimental Chapel. If a Visitor said they wanted to attend a service or Office at Carlisle Cathedral, even as a devout worshipper I would try to find out where it was to be held, as it would make a subtle difference. It even does to me (and I have been to Mass or other Daily Office at Carlisle scores of times, sometimes the only member of Laity present), even if ultimately I just want to go to 8am or whichever service. Likewise at almost any UK Cathedral I can think of. Doubtless at St Peter's each Chapel has it's own particular history, and unique fixtures and fittings.
Even at St Paul's Cathedral in London I have been to Morning Office and been the only Lay Person present. I doubt that ever happens at St Peter's.