Here's something to try. Go to Google Flights, enter your airport for departure, enter Anywhere for destination, enter dates. Different ideas and prices will come up. It may be a start.

P.S. What cities are all of you in? There may be a connecting city in common.

Pick a few destinations that the group might like, then run a sample booking for the person flying out of the least served regional airport for each. If any fit your budget, then test from other member's departure cities.

You aren't going to find a single search engine that lets you enter four starting cities plus a maximum spend. That starts getting beyond the capability of the average algorithm used by booking systems.

"find destination options within a certain budget"

Difficult. In your place, I would look for distance. Distance and ticket price do not directly relate, but there is still a logical connection.

To make your task even more difficult. Direct flights can be more expensive than indirect flights. Therefore, if you change the routing, the ticket price can drop.

Hand luggage only flights are cheaper, as well. But not everybody is able to travel light.

Obviously avoid peak travel times to reduce the costs and try to book reasonably in advance.

Finally, you can always balance a bit with the cost of the accommodation.

I think ultimately you'll have to compare the costs for each journey to the destination. Maybe your friends can do the research themselves

One very useful function is to google "arrivals " and the name of the potential destination airports and you can see what cities you can fly from direct

If you want responses from random folk on this forum, at least give us a hint of which country or geographic region you all start from?

How many hours are you willing to fly? How long would such a trip be?

What time of year? Do you want cold or hot destinations?

Are you after beaches, city, hiking, mountains and lakes, museums, temple bashing, water sports or what? Or don't you care, just flight price?

If it's just random, some of the above points may be more relevant, but it's not the way I consider starting with travel plans.

SWT

Thank you all for your responses. I'm not looking for specific travel suggestions, moreso to understand if there's a site or app to make group travel planning easier that I'm not aware of.

Many airlines have a website function that allows you to input a departure point, but not a destination. They then show you one, two, or more stop destinations and the current price associated with them.

'to understand if there's a site or app to make group travel planning easier that I'm not aware of.' Without some set parameters you're asking how long that piece of string is versus this piece of string.

Fares are changeable, and fares purchased today from four different cities to Somewhere aren't necessarily going to be available for sale tomorrow. I can't see how four travellers from different origins could be put on a single booking as I don't think a carrier's GDS would be able to construct it.