Your "must sees" and "must dos" are your own. Without knowing what you really enjoy, it's hard for strangers on a travel board to tell you anything is a "must see".
If you are new to traveling in Europe, start by realizing that you need to give yourself a bit of time to get your bearings in each destination you choose and every time you have to pack up and change locations, you are losing time. Don't be overly ambitious and plan way too many stops in an attempt to squeeze all of Europe into 8 weeks. If you move too fast hopping from place to place, everything starts to blur together and you won't remember much about any one particular spot. It can also become physically and mentally exhausting as you are doing this solo and you have no one else to rely on but yourself to help you plan this or get from Point A to Point B.
Be flexible with your plans - realize not everything is going to work out the way you might want it to. Don't choose too many far flung countries if you are trying to keep your costs down. Don't fly round-trip in and out of the same city/country even if the airfare seems like it is "cheaper" unless you first factor in the transportation costs to get back to your original point of entry - open jaw often works better and can save you money and time.
I try to go by a loose rule that each country should receive, at the bare minimum, 1 full week (preferably 2). If you go by this, in your 2 month time frame, you just need to accept you aren't going to see it all. This is especially true if you are hoping to mix in both big cities and small, scenic towns. A single week in a country will at least give you the time to experience one of the main cities, and then have a few days to spend outside of the city. Again, this is just a general guideline - a huge city, like London or Paris, is full of so many things to see and do that you could sometimes easily spend an entire week there and still barely scratch the surface.
How do you plan to get yourself to those small, scenic towns you would like to see? Are you getting a rental car or are you relying solely on public transit? Don't forget that crossing international borders with a rental car can often be pretty expensive - you will want to plan out when you will truly need to have a car, and when you won't (ex. you don't want a car when you are staying in Paris, but you likely will want one if you are headed over to Normandy).
I'd go for countries that share borders and maybe save the outliers for another time. Just as an example, in 8 weeks, you could do something like fly into Rome, spend your first 2 weeks visiting Rome, Florence, Venice and 1 other part of Italy (Tuscany or a coastal region), head over to Vienna and spend Week 3 in Austria, move up to Prague and have your Week 4 in Czech Republic, maybe spend Week 5 in Germany, Week 6 could be split between the Netherlands and Belgium and you could either spend Weeks 7 and 8 entirely in France and fly home from Paris, or else carve 5 nights out of that final Week 8 and take the Eurostar from Paris up to London - this is about enough time to get a very limited overview of London itself and maybe squeeze a single day trip in outside of London. Normally, it costs more in fees to fly home from London, but depending when you are traveling, you might want to hit Italy before it gets way too hot. Keep in mind that if you are traveling during August, that's a really busy time for a lot of Europeans to also take their own vacations, so you may find budget lodging harder to find if you are visiting coastal regions during August unless booked well in advance (particularly in France and Italy).
