We did the Baltic with NCL last summer and it was the trip of a lifetime! In fact, we plan to do it again next summer - too much to see in one trip.
I do not know the exact itinerary with Princess but I think it's pretty similar to NCL's.
We are advocates of doing DIY walking tours unless there is something outstanding to see and used Rick Steve's books to outline those.
We also used the hop-on/hop-off buses in many locations. I found that if you save your tickets from the previous day they give you a 10% discount on your ticket the next time. Most countries allowed you to use your credit card but one did not (I think it was Denmark).
One of our favorite places was Tallin, Estonia. Remarkable how preserved the town is. You can easily do this on your own. Wander in and out of old churches and shops and the Orthodox church is magnificent!!!
St. Petersburg of course is the jewel of the trip and I wish they spent 3 days rather than 2 there. Ships tours are recommended because of Visa requirements although 2 couples on our trip booked on their own and loved their experience. I think if you go to the destinations board you will find reference to the two agencies who do that. Anyway . . . I was overwhelmed at Catherine's Palace and Peterhoff. Church on Spilt Blood is breathtaking and the Hermitage is just not to be believed. Soooo much to see in so little time. If you are an art lover you should spend an entire day in the Hermitage, it is huge. The best flea market in which to buy icons (reproductions of course) matruska (sp?) dolls, etc. is in front of the Church on Spilt Blood.
In Helsinki be sure to see the Church in the Rock. It is a Lutheran church carved into the hillside that is very unique. There is usually a local musician playing soft music there and a nice place to sit and rest your feet.
In Stockholm there is a place whose name I don't recall, but it is billed as an outdoor museum of history, that is a wonderful experience. You can walk through village areas and watch glass blowing or carpentry with antique tools. You can see animals and housing from different parts of the country. It was a lovely stroll that filled our afternoon and we only saw parts of it. It was on the hop-on line so getting there was easy. They took credit cards for admission and we had a nice lunch there as well.
Tivoli Gardens is a big billed item in Copenhagen and while it isn't Disney Land as is often portrayed it is very nice. Beautiful flower beds and lots of free entertainment. We listened to a beautiful strings concert then a big band. We saw terrific acrobatics a la Cirque de Soleil (sorta). There are plenty of restaurants and bars although they were all quite full. We enjoyed having a glass of wine and dancing on the pavement.
Be sure to dress appropriately. We were there the first week of August and found the weather could go from tee-shirt to sweatshirt in a flash.
I found long-sleeved t-shirts to be ideal, a travel vest (yes, it looks touristy but I am one so what!) and a sweater or sweatshirt. A waterproof jacket or poncho is wise as well since it threatened rain every day in Scandanavia but only made good on the threat one afternoon.
The north Atlantic is quite rough so if you need meds for motion sickness have them handy. We transited the Kiel Canal so we only had one rough night.
I think you will find this a fabulous trip. Buy some great guide books and choose wisely in St. Petersburg, although it will be tough to decide!