Hi Laura,
Long time Edinburgh resident here! Fringe time in the city is a bit of a scramble so this is the right time of year to be beginning to plan, but don't be surprised if the locals aren't in the same rush you are - their spots will all get filled regardless of the time they put them on - it's just the nature of the beast. As in all cities the closer you are to the city center, the pricier. I'd also be aware of the locations of the 'Edinburgh Festival' (separate to 'Fringe') venues since they'll also be desirable locations/booked by large ensembles and big budget shows. I wouldn't think for 27 you'd need to book a hotel, but if you all want to be together then it may be your preferred option - that or one of the University campus'.
Specifically, I'd recommend triangulating your venue with one of the major routes into the city, and check for listings along that route. Public transport in Edinburgh is fantastic and reliable and affordable, so I wouldn't gawk at being up to 20-30 mins by bus or tram away from your venue. That way you'll have a much broader array of options, and hopefully won't get too gouged.
Sorry I can't be more specific. In my many years of performing at the Fringe I never had to find accommodation, so I'll leave it to the rest of the hive mind to provide specific recs! But if you need anything else feel free to reach out.
All in all, I hope you have a fantastic experience, it's great city, and in my opinion, a singular energy during festival time!
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Joe Revell
VA
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