two very chill grad students looking for a greek island for a few days??

Naxos or Paros, why not...

Both have a good bus service, easy to reach from Athens, quite a few beaches, villages, hiking options, however they are extremely touristy and in August will therefore be crowded (and expensive).

With the same advantages, a little less crowd, but even more “Cycladic” than Naxos and Paros, see:

• Sifnos

https://www.roomsinsifnos.com/

With fewer buses, even fewer crowds and close to Athens:

• Tinos

https://www.visitgreece.gr/islands/cyclades/tinos/

• Kythnos

https://www.kythnos.gr/en/

• Serifos

http://www.serifosisland.com/

*Naxos and Paros: 7 to 8 ferries per day. At least 10 flights per day from Athens.

Sifnos: 3 to 4 ferries per day, no airport.

Tinos: 7 to 8 ferries per day. No airport.

Serifos: 3 to 4 ferries per day, no airport.

Kythnos: 3 ferries per week, no airport*

Whatever your choice, leave for the island as soon as you arrive in Athens and save Athens for the end of your stay.

More information on the official Greek tourism website:

https://www.visitgreece.gr/islands/cyclades/

If you plan to go hiking, be very careful as several people have already died this summer due to heatstroke on a few different islands. Athens too has been super-hot, unseasonably early.

We spent a week in Naxos this May. Beautiful island and beaches. Island bus transportation. Don't drink the water. There are several ruins and ancient sites. We stayed in Naxos Town and had fun exploring Old Town. There are 10 hiking trails on Naxos. The Greek residents are very friendly. Food/drink are insanely inexpensive...but delicious! It was very windy, so that may give you respite from the baking heat (although in May, it was cool). We've recommended Naxos to family and friends.
Good Luck!

we're doing a few days in Athens and then a few days at an island

Better if you spend the end of your time in Athens; best advice is to be in Athens the night before your return flight.

You might want to consider Kos. They have some bike paths, and lots of bike rentals. Also, its close to Turkiye if you want to take a ferry over for a day.

Beaches were nice and the water was super clear. Lovely island.

Good Luck

I will not point you to a specific island, as each one has its pros and cons, but I will give you some general advice that will come in handy in whichever destination you pick.

Water
On most islands the sink water is desalinated, so get used to drinking only bottled water. In theory, it is ok for cooking, but NEVER EVER try boiling pasta with it!

Transportation
It varies from island to island, but generally, a scooter is half the price of a small car, quad bikes cost as much as a car (or more, depending on the size), and 4x4 is more expensive than everything. Most islands have a decent network of buses covering the main beaches, but remember that in the Greek islands, you can usually flag down the bus even if there is no stop nearby, which is handy to cover smaller places that might be snuggled between stops. Taxis in the smaller islands don't have a meter, instead, they have (somewhat) fixed prices for each destination. Also, remember that from/to ports and airports there is a surcharge.

Travel

Wind is always an issue in the Greek islands. If your return trip to Athens is with a small vessel, you might have to scamper to change tickets at the last minute or even have to change your flight. As such, it is always better to be in Athens the day before your flight. Leaving the tour of Athens for the end of your holidays is the best option, as you will not need to worry about the weather.

Boat tours

Most boat tours are overpriced, in part due to the high cost of the needed fuel, but in general, catamarans are the most expensive and overcrowded, Sailing boats take 8-10 passengers max, catamarans 40-60. check with the fishing boats as well, in the last five years the government permitted them to take passengers. They usually do tours which might include a bit of fishing, the deck is more spacious than the sailing boats, and being faster than the sailing boats gives you more time to explore/swim. Finally, there are small motorboats that you can rent by yourself without needing a permit. Remember that the fuel is never included in the price.

Hope this helps