Road trip across Central/Eastern Europe.

SJ, Yes, this is feasible. But whether it is the best option is another question.
Prague, Bratislava, Budapest, and Split - 4 places in 13 days, that is reasonable. But, why are you flying into Vienna if you don't plan to visit Vienna? Why not fly into Prague?

A car is usually a liability in most European cities. You will end up parking it (and paying for parking) and then using public transport in the cities. But, if you want to spend most of your time visiting the countryside between these cities, a car is a good idea.

Yes, a hire car is usually allowed to be driven in most countries in Europe. You should tell the hire car company when you book which countries you plan to visit.
But, where are you flying out from? Hiring a car in one country (Austria) and returnng in in a different counry usually has a high surcharge.

And, as part of your preparations you need to make stimates how how long (Hours) each part of the trip will take, and how much it will cost (fuel and tolls). You can do this on: http://www.viamichelin.com/

P.S. "I, along with 4 of my friends" - that is 5 people in one car, plus their luggage. You will either need a large car, or 2 cars. Most cars are 4-seaters, and you cannot fit 5 cases in the boot.

I have been to all the cities you mentioned, except Bratislava. Like the previous comment, not sure why you skipped Vienna.

Split is an interesting city, but not sure it is worth the drive from Budapest. Dubrovnik is more interesting that Split. I am an ancient history buff and had to see Diocletian's Palace in Split. It was interesting as well as a city north of Split called Trogir. Still, Vienna beats Split hands down. You could probably handle visiting Prague, Bratislava, Vienna and Budapest taking the train. To get to Split you probably need a rental car.

You might look at taking a river cruise that includes your cities.

Agree with above answer, been to all cities excep Split. Is is too far to drive, concentrate on Vienna, Prague, Budapest. All great cities. One day in Bratislava would be sufficient.

Hello sj.1802. Traveling, in a car, from Budapest in Hungary to Split in Croatia would be very time consuming and not very pleasant, I think.
13 days in Europe is not much time. I recommend that you travel to
Prague
Vienna
Budapest.
And, I recommend that you travel in Railroad trains, not in a rental car.

Split is750km from Budapest, so a long way from the other places you mention. A road trip with five of you in one car sounds uncomfortable by any measure. With 13 days I would pick a maximum of four locations and take the train.

Berlin or Munich
Prague
Vienna
Budapest

Thank you all for the replies.

@Chris F - We can change the itinerary a bit and fly to Prague. Tickets were substantially cheaper for Vienna and the distance between the two did not seem to be a lot on Google Maps.

Our plan was for a road trip as it adds to the fun and excitement of the trip, I guess. We will be picking up the car from Austria/Czech and dropping it in Croatia. Will they charge a lot for it in this case?

Thank you for sharing the website link. Seems helpful.

I too was thinking that a trip this long with 5 in a car (with our Indian size luggage) might not be the best idea. Will probably look for a bigger car but that would mean an extra headache at the time of parking and drive in the cities.

@geovagriffith - Vienna does not seem to offer a lot. It seems like a city where you lay back and enjoy the views. We were thinking of a city which has more to offer in terms of adventure or nightlife. That's why we weren't that keen on Vienna or Austria.

We added Dubrovnik now as inter-Europe flights are cheaper from there. Also, that's the Kings Landing city and I would not miss it. Split was added as we can do some water based adventure activities there and have also read a lot about its night life.

@Ron - Are railroads more convenient? We want to keep the trip a bit open ended and not restrict ourselves to any schedule. Don't think railroads can offer that much freedom. Or can it?

People have reported rental-car drop fees up to US $500 or more, but it's an individual thing. You might be luckier. It's something you need to check before you are committed to renting a car.

It's possible to see all of these cities by driving but not the easiest or the cheapest way.
Agree with the previous posters about skipping Split on this trip...too far out of your way for such a short trip.
Car rental companies will ALWAYS charge you a very hefty fee for dropping a rental car off in a different country than the one where you rented it...hundreds of dollars.
There is absolutely no advantage to having a car in any of these three cities. We were in all three of these cities last summer with a car (my husband had some severe ankle issues and couldn't navigate trains or train stations) so I'll share my experience with you.
1) Paying to park in these cities is expensive. Prague is the cheapest of the ones you list and will run you somewhere around $30 per day to park in a clean, secure garage. There is virtually no street parking in European cities...it's often by residential permit only.
2) Once you park the car in any of these cities you won't use it again until you leave to go to the next city. Do you want to pay for the rental and for parking when it's just sitting there?
2) Driving in big cities can be extremely challenging and there are restricted zones that aren't always clearly marked...you will receive a ticket in the mail months after your trip if you accidentally drive in one. There are also many one-way streets, lots of construction, bus zones, and a lot of congestion.
3) You're not just paying for the rental car...you're also paying for gas (quite expensive in Europe), parking, and tolls. You'll need a toll vignette for the Czech Republic, Slovakia, and Hungary. These are available at clearly marked vendors at the borders...not super expensive but it's just one more thing you'll need to pay for.
For this trip you really should be using trains. There will be plenty of room for you and all of your things and you'll be much more comfortable and less stressed when you arrive at the cities you want to visit. If you buy your tickets ahead of time they won't be expensive at all.
Addition on 8/7...One other MAJOR factor can be truck traffic...some of the border areas in eastern Europe have checks for long-haul trucks and these can cause huge jams, especially at the Hungarian border. One more reason to use trains!

The BBC radio show, 'From Our Own Correspondent' (starts at 22:22 min:sec) recently had a report from the Balkans on long delays, several hours, at some Balkan border crossings. You might be able to use something like Google maps or Waze to monitor delays at border crossings.

And Guy De Launey, caught in a summer holiday traffic jam on the border between Serbia and Croatia, reflects on how far the two former entities of Tito's Yugoslavia have fared in the twenty-five years since war split them apart.

I would suggest using the train and the bus (even buses from city to city) as the means of transportation. Forget the rental car. I don't like paying for gas by the liter.

In Split, i would suggest you to take a taxi. In summer (i suppose your trip will be on summer) it is huge traffic and Split have a good night life, so it would be not so smart cruising around after good party. So, take a cab and enjoy... :)

So you decided now that you will arrive to Prague. I think you will like it there. It is a party town more than Vienna and Budapest. Very good and cheap beer. Prague and Budapest are eye candies. Vienna is grandiose and classical. But you decided to skip it. You got 13 days. That is not much. My recommendation would be to skip Split. It is too far away and getting there would take too much time. So it looks like 5 days Prague (in reality 4, don't count the first day when you are tired after a long flight and also jet laggy). If you want, nice day trip would be Kutna Hora (historic silver mining town). Or some other day trips; see Rick Steves book: Prague & the Czech Republic. Then forget a car and go by train direction to Budapest. That's a long ride but you can have a break (1-2 days) in Brno (also party town) then another one in Bratislava (they say - and I agree - that there are very pretty girls there) and then continue to Budapest. Wide boulevards, wide Danube River, wide beautiful views, good spicy food - they invented goulash and good wine from Tokay region. Fly back from Budapest.