Feasible itinerary?
 

So I'm planning a trip with my family (4 adults in total), and I was wondering- on a budget of $8000, is it possible to visit Prague, Venice, Florence and Rome in 10 nights? We don't mind staying in hostels or making compromises like that.
I'm not asking anyone to plan this for me or anything, I just need to know if it's possible or if I'm totally reaching for the moon here.
Thanks!

Plan to lose about 1/2 day every time you move to all the logistics...so with 4places that is two days out of 10 gone. If the 10 days includes travel days to and from say N America you are down to 6 full days of enjoyment for 4 locations.

I don't like wasting that time and cost in logistics and travel so I would pick two places and spend my time enjoying the two places rather than racing around trying to see too much in too little time...

Venice, Florence, and Rome would just be possible, although you'd only get a brief glimpse of them. Including Prague would make it a whirlwind, unless you have a magic carpet. Even fairly short trips, such as Florence to Rome, end up wrecking a whole day for all practical sightseeing purposes. You will have nine full days on the ground, three of which will be consumed with travel and logistics.

If you decide to visit just Italy, I suggest you spend four nights in Rome, which is the bare minimum to do more than check some "must-sees" off your list. Rome is a big city, with many things to see, and it's a city that should be experienced, rather than seen. That would leave you five nights to split between Florence and Venice. The division should be made dependent on your interests, and whether you want to take any day trips from either city.

Does the $8000 need to buy 4 people plane tickets? And if yes, from where?

Or that's your budget for on the ground only... hotels, meals, transportation, admissions, etc.

You could fly open jaw Venice/Rome or vice versa, train to Florence on the way.

Or eliminate Venice. Fly Rome/Rome. Upon arrival, get to the Tibertina train station, buy tickets and take the 1.5 hour ride to Florence. This may make more sense if you only have 8 days on the ground.

WOW thanks for the fast replies!
I wish it weren't so expensive to simply get to Europe, or planning trips wouldn't be such a problem.
Now I have a good idea of what I should be doing and what to expect.

And if you look at air costs out of PRG, you'll quickly eliminate that city. Much too much for 10 days. Venice (3 days), Florence (3 days), and Rome (4 days) should be a good trip.

I agree with above--Venice, Florence Rome in that order. Italy is easily to overdose on food, culture, art, history and architecture.
Travel between each city is by fast train, and reservations are required. Trains are cheap, fast and efficient.
See RonInRome.com for the best travel info there is on Italy, and especially Rome. He also reviews some rooms in Rome.
I usually use Booking.com for accommodations--filtering for lowest to highest prices. Then I look for properties getting high customer ratings. I also sometimes look at TripAdvisor.com to see what has been said about properties I'm interested in staying at.

It comes down to the adage about stopping to smell the roses. Trips are not fun when they are so rushed that it appears more about checking destinations off of a list of places you have seen. You will not have time to enjoy anything at that pace. I would highly recommend that you skip Prague this trip out. You will feel rushed just trying to spend time in Venice, Florence and Rome.