Travel to Austria and Czech republic
 

My family want to to go to Austria and Czech republic but not with a organized tour.
What we want is to fly from Toronto to Prague, Czech republic go around move on via train/bus to the next country (Vienna & Rome) until we're done the countries mentioned and fly back.

Which is the best way to visit these countries via train or bus?
Is possible to do this in 2 weeks?
how much money am I looking at?
plan to make the trip by last week of May up to first or second week of June..

It's certainly possible to do 3 cities on 2 weeks - but if you mean the last week in May - as in a month from now - you have left it very late for plane tickets and hotels - and deals will be long gone.

Without knowing where you are coming from I would assume air fare into Prague and out of Rome is about $1100 per person with a connection each way (not sure if flights without connections are possible).

As for the rest of the costs - you need to tell us a couple of things:

How many and who in your family - so how many hotel rooms you need?
What level you travel at? Strict budget, modest, moderate or upscale (are you willing to do B&Bs with shared bath and stairs versus elevator - or are you looking for 4* hotels with AC and full service)

You can travel at almost any budget level - if you are willing to live at that level (picnic with food from a market versus a sit down dinner with wine at white cloth table)

It is easy and comfortable to travel by train from Prague to Vienna. If you buy your ticket online and in advance it costs around 20 EUR:
Czech Railways - https://www.cd.cz/eshop/
From Vienna to Rome you can take a night train.

Trains are by far the best way via public transport between large cities like Prague to Vienna and on any long distance trek - buses usually just fill in the gaps where trains don't track - for lots of great dope on European trains I always spotlight these IMO fantastic sites - www.seat61.com; www.budgeteuropetravel.com and www.ricksteves.com. If traveling on several longer trains investigate the Eurail Select (Saver if two or more traveling together) Pass valid in up to five countries.

I've taken the overnight train Vienna to Rome/Venice/Florence several times - it is one of the better night trains in terms of comfort, etc. Save on the cost of a night in a hotel and daytime travel times - even flying takes a half a day no matter how long the flight.