Need Ideas for University Trip

The UK. Ireland. Istanbul.

Italy. Should be nice in April. Into Venice and out from Rome with Florence in between.

I had the idea of Athens-Thessaloniki-Istanbul but wonder if it's too much traveling/too far from each other...

I suggest looking for airfares first, since that's likely the single largest item in your budget. I don't know your starting point, but right now Google Flights shows roundtrip economy fares between Seattle and Paris in the $600 range for April dates. Do some more exploring, using your actual home airport and looking for the lowest fare that takes you somewhere that meets your needs. Nonstops are easiest on the body. You may save money by using connections, but consider whether the saving is worth the added time and stress.

Moving around overseas costs time and money. Your budget will go farther if you choose a single base city, or maybe two. If you choose two bases, set up your flights to land in one and leave from the other ("open jaw" or "multi-city" itinerary). That will cost little or no more than a round trip, and save the time and cost of backtracking in Europe.

Besides airfares, consider costs on the ground, especially hotels. For example, the UK, France, Switzerland, and Scandinavian countries will cost more than Spain or central/eastern Europe. As you consider Greece, you may find a tradeoff between higher airfare and lower on-the-ground costs. This website has good advice about trip planning, though it's geared more for ordinary tourists than a student group.

Lucky students!

Consider the various exchange rates against the USD. The UK GBP will cost you more than the USD against the Euros. The further you go in Eastern Europe (now Central Europe.) the cheaper costs are.
Have a great trip!

Given the philosophy behind the trip and budget; Istanbul. More cultural revelations, less expensive than most destinations.

What are psychology students interested in? The options are almost endless. But I do agree that Berlin is not a bad choice.

But Scandinavia does not have to be expensive, with a group it can be done one a reasonable cost.

Spain: Madrid, Granada, Seville

I would suggest either Berlin or Paris.

Focus on visiting the various culture and historical sites in each city, such as in Berlin sites connected to Prussian history, the more esoteric the better, the Imperial era prior to 1914, obviously, Weimar Germany, then Nazi and Soviet totalitarianism sites in Berlin, the Cold Era. Let them go to the DHM (German History Museum) on Unter den Linden and critique the presentation of the historical periods displayed, the focus, the concepts presented, etc.

It is an admirable goal you have set : "immerse ourselves into something different" Given your time constraint, I would suggest prior to this trip that the student make some genuine efforts in acquiring some of the local language, even snippets are better than nothing at all, without having immediately to lapse into English.

Your money will go further in Spain or Portugal than in Germany or the UK. What quality level of accommodation do they need? Eg will they share rooms, need en suite. The budget isn’t massive but will be possible.

These are all great ideas.

Scandinavia is out because one of my students is from Scandinavia (but maybe for a trip another year).

The students are willing to do dorm-style lodging to stretch the budget, if necessary. So youth hostels can work.

They would love to go to Italy but many of them have already been there (they don't care but I think it's less of an immersive experience if many have traveled there prior).

You could always do London and Paris.

Poland. Inexpensive, date I use the word cheap. So much interesting history, fly into krakow out of Warsaw.
Berlin is another great choice, enough to see and do there for the entire 10 days.

"So youth hostels will work"

In Berlin there is another level of accommodation if you prefer not using the youth hotel option. Berlin has, aside from DJH hostels and private, independent hostels, also Jugendgästehäuser. This sort of accommodation, the Jugendgästehaus, I believe, would be more suitable to your students.

If keeping expenses and cost down is a major concern, be advised that in Berlin one (outsiders) can have lunch at the Mensa (indicated in big letters) located on Hardenbergstrasse with walking distance from Bahnhof Zoo. This site is part of the Tech Uni. the TU. Pre-pandemic I had lunch there a couple times. At that time no ID or anything likewise was asked. Good cultural experience in Germany, you'll see the diversity, and certainly fits into the aim of "something different."

Well, admittedly, my visits to the TU Mensa were ca. 10-13 years ago. I was told then that Humboldt Uni did not offer this lunch option as did the TU but I never checked it out so I don't know exactly.