To find accommodation for your exchange in ESADE, first, you should check in which ESADE campus you’re going to study. There are 2 campuses: one in Pedralbes, in Barcelona, and the other one in Sant Cugat, a small city at 30min in train/car from Barcelona. So you should take that into consideration when looking for accommodation.
If you’re studying in the Sant Cugat campus, you can still live in Barcelona as it is not that far away and in general, people tend to prefer living in Barcelona as
1) There is more options to find a place and
2) There is way more stuff to do in Barcelona and it’s easier to go out!
However, if you’re studying in the Sant Cugat campus and you choose to live in Barcelona, you should look for a place near a ferrocarril station (see "Move around Barcelona like a Pro") in order to access easily the campus.
The best neighborhoods to live in Barcelona during your exchange are:
Sarrià
The closest to the campus of Pedralbes, not the best neighborhood to experience the life in Barcelona, not a lot of stuff to do and also definitely not the cheapest but there is a train station nearby and it’s easy to go to the center of the city.
Gràcia
Feels like a small village in the heart of Barcelona, very cute with small streets, lots of bars and restaurants, lots of students living there and there is a train station nearby
Les corts - Sants
Also close to the Pedralbes campus, pretty cheap compared to other neighborhoods in Barcelona but no ferrocarril station nearby
Eixample (Left & Right)
Located in the center of Barcelona, really nice to live in, lots of bars and restaurants, great atmosphere. There is a ferrocaril station nearby (depending on where you live exactly), can be kind of expensive.
The rest of the neighborhoods are either too far away, doesn’t have good public transport connection to the campuses or are too touristy.
Make sure to check this post "Best Websites & Apps to find apartments in Barcelona"!