@foxymom, I'll tweak your itinerary a little ha. Here's how I'll do a 17-day trip:
Day 1 Arrive FRA and stay overnight at a hotel near the airport.
After checking in at your hotel, hop on the train to see a little bit of the city.
Day 2 FRA-PRG via Czech Air
Day 3 Prague
Day 4 Prague
Day 5 Prague (whole day).
Take the overnight train EuroNight at 11PM to Budapest. A 2-bed sleeper compartment with
private washing facility will cost you approximately EUR150 for two persons.
Total: 4 full days in Prague
Day 6 Arrive Budapest at 6AM.
Day 7 Budapest
Day 8 Budapest
Total: 3 full days in Budapest
Day 9 Take morning train to Vienna. Train travel from Budapest to Vienna is roughly 3 hours.
Arrive Vienna in time for lunch.
Day 10 Vienna
Day 11 Vienna
Day 12 Vienna. Take the overnight train to Florence at 9PM (connecting at Venezia Sta. Lucia Mestre).
Total: 3 full days in Vienna
Day 13 Arrive in Florence at 10AM.
Day 14 Florence
Day 15 Florence
Day 16 Florence to Milan via train. Train travel is roughly 2 hours.
Overnight at a hotel near the airport.
Total: 3.5 days in Florence
Day 17 MXP-MNL
It's a little bit too hectic for my style of travel but definitely doable. I haven't been to Budapest yet but vhanya is correct ideally try to spend at least 4 full days there so you get to visit most of the attractions. I heard there is a certain old statue there that looks like Woody Harrelson.
Vienna, I love Vienna! I was fortunate enough to visit for a little over a week when hubby was on training. For me ha medyo bitin pa ako sa one week but if you just want to see the major sights pwede na 3 full days. Don't miss the Belvedere where you'll find Klimt's painting The Kiss. On shopping, if you like Swarovski, this is where you can hoard since it's from there.
I bypassed Milan altogether since your concern is to get to Florence (for the shopping!!!). You have 2 full days to see the city while one whole day to go to the outlets. Or skip the city and just shop! Haha! Kidding aside, you have to see Florence. It's a sin to go there and not visit the attractions.
I'm so inggit! No Europe trip for us this year

Hopefully next year.

Enjoy your planning!