Hello, a slightly belated welcome to Lonely Planet and Thorn Tree...
I don't know if you've noticed there are destination guides on the main page of the LP site, here's the link to the section on Corfu for the basics and for helpful tips.
https://www.lonelyplanet.com/greece/ionian-islands/Corfu
Here are other guides
http://www.corfuvisit.net/default.asp?id=4&mnu=4&LangID=English
http://wikitravel.org/en/Corfu
What I would suggest, rather than a hotel which may not want to accommodate your entire party (which if it were small
might take up all of their facilities--and they may have already booked rooms for July) is to look for a house or houses where you can all stay. While a hotel might provide the food, if you rented a house you could either cook for yourself or perhaps arrange for a cook.
Here is one I came across which can only handle 10 people but it offers so many other amenities, you might consider it and find additional lodgings:
http://www.castelli-cottage.gr/en/photogallery
Here's a site with has info on the northern part of the island, with the link directly to lodgings:
http://corfunorth.com/index.php/en/accommodation/
You could also check Airbnb.com as I see they have a variety of listings.
Here is the link for VRBO which is long established and forum members have given the rentals they've used good ratings
https://www.vrbo.com/vacation-rentals/europe/greece/greek-islands/ionian/corfu
And to help you sort things out, here's a site with the towns so you can locate where things are:
http://corfugreece.net/content/view/22/29/
You haven't said what your budget was so I'm providing as many options as I can so you can explore what is there.
Just remember it's prime (high) season so everything costs more (lodging-wise). Only posh places will have their
own private quiet beaches.
Good luck with your plans, would like to hear how things go...and if you have any suggestions or recommendations when the trip is over. Thanks