Here's my favorite comprehensive website on Milos. http://www.milos-island.gr/index.en.html To explore, you'll really need to rent a car ... bus system very sparse ... cars cheap (€35?). YOu don't say what the age of your daughter is. If she's 7, it's beach & bucket, if she's 17, cafes & nightlife more important! For nightlife, it's all in Adamas in June, but that's not the place for swims ... but with a car u can go anywhere. I stayed w. my friends in Pollonia, dozens of places right on or just off the beach, also has several tavernas, a bakery, a grocery etc. http://www.pollonia.com. We stayed at Capt. Stavros, there are many like i -- all are very straightforward, family-run places, not much english, great views. http://www.milos-island.gr/rooms-apartments/pollonia.html There are I think TWENTY-TWO beaches in Milos, BEACH MAP http://www.milos-island.gr/beaches/beaches.html Some have no amenities (sunbeds, food etc) Here's 1 of many guides to Beaches http://www.cycladia.com/best-beaches-greece/milos/?res_perpage=25
The boat trips around the island rim are full-circle or half-round; I favor the latter, from Adamas to Kleftiko & back -- more time to go ashore in several coves for swims, BBQ ... rubber raft trip thru natural arch/caves. There are big party boats in hi season; in June just small (6 pp) sailboats, one big catamaran (cap. 14); we took latter & loved it. The advantage is -- even if it's windy, the cat can go under sail, where small boats have to just motor. The boats line up in port before dinner, you "shop" and choose.
Do NOT miss the Mineral museum in Adamas ... yes, lots of minerals but main thing is color doc. about miners & mining (men & women) over past 100 years... interviews, stories, very moving. Memorable insight into a culture, a people.
Also the ancient ruins & the catacombs well worth a visit... and Plaka (the high town) , stunning views!
Have a wonderful time ... have been there 2x would welcome a re-visit-- TJ