Looking to travel in October starting in Copenhagen then Stockholm and ending in St Petersburg , all new areas to us. We are trying to stay away from a cruise as we like to be flexible as we travel. How many days would each city take and best way to travel between cities, train or flight?
From Copenhagen to Stockholm, you can take a train or fly (locals mostly fly). From Stockholm direct to St. Petersburg, it's easiest to fly, but you could also go the slow and scenic way: overnight boat to Helsinki, then boat to St. Petersburg. The advantage of this is that if you take the St. Peter Line boat from Helsinki, you can spend several days in St. Petersburg without needing a visa and without needing a pre-booked tour. If you go any other way, you need a Russian visa (expensive and a hassle to get). If you're getting a Russian visa and are going to Helsinki, you can also take a new fast train from there to St. Petersburg.
How long in each place? That's up to you. I'd say each city needs 3 nights minimum, but that's minimum; there are certainly ways to fill more time. One thing to consider is that, while it's easy to return to Copenhagen and Stockholm, the need for the visa means that you probably won't be returning soon to St. Petersburg, so you may want to allot more time there to make sure you see everything on your personal must-see list.
A good way to start figuring out how long you'll need is to look at Rick's lists of top sights for each place, then read more about them and see which ones interest you. For each city, click the "At A Glance" tab to see his lists (again, they're just his opinions, but it's a start):
Stockholm: http://www.ricksteves.com/europe/sweden/stockholm
Copenhagen: http://www.ricksteves.com/europe/denmark/copenhagen
He doesn't have an "at a glance" list for St. Petersburg. But if you look at this website from a Russian company that works mainly with cruisers, it will show you what they consider the highlights for that clientele (look at the 3 day itineraries to see more places): http://www.alla-tour.com/tours/
Visited SPB this summer with a visa. It was an expensive, tedious task to acquire, but well worth it to us. We took a hydrofoil out to Petershof (Summer Palace) one day, and it the cruise ships piers are WAY FAR away from the main city part of SPB. Much better to get the visa. We thought the Silja ferry line was very nice, and the accomodations for overnight travel from Stockholm to Helsinki look great. It is like a mini-cruise ship, so you can take that and know you will have plenty of restaurants, etc onboard and comfortable sleeping rooms. In Helsinki you can take the Allegro fast train to SPB. It is clean, safe, economical, efficient and gets you a much better view than an airplane. We stayed at the Pushka Inn in SPB. It is just steps from the main square of the Hermitage, the piers for boat trips, and the "main drag" of Nevsky. Highly recommend this hotel. As an added bonus, the included breakfast is at the restaurant next door which has other meals that are of good quality and modest price. If you would like specific ideas about things to see/do feel free to PM message me. We have also been to Copenhagen, and traveled with a rail pass from there to Germany. It included the most unique trip ever, which was having our train car load onto a ferry to cross the sea. Quite the amazing experience.