Abby, thanx so much for details that enable us to help you - Now, if ONLY the RS site would tweak software so we could reply while also seeing past messages!!! Currently when one hits "reply" everything vanishes but original post. Thus, I must have 2 screens open. Grrr. Anyway, since what you want "quaint & clean" & economical rooms. For 4, you hope no more than 125 per night -- assuming that's $$; it means €102. BTW, it's thoughtful to quote in Euros, too; use this quick site- http://www.xe.com/currencyconverter/ Thats $60+ per room in June; doable in Naxos, u may have to go UP in Santo/Athens. But I can help if you act TODAY; do not dither! Here are the AREAS I advise for your bunch (u + mom + teen girls), AND my best bargain Gems -- I have checked them on booking.com for availability --- However, if you contact them DIRECT, (and DON'T fill out a form, write a very courteous E-MAIL, compliments help, and tell what you want. They save the agency % fee, and they'll love you all the more. Normally if you book direct, u get best rate with no deposit & cancellation w.o. penalty if you give sufficient advance notice.
SANTORINI - FIROSTEPHANI - http://mapsof.net/santorini/thira-island-santorini-map - This is the "goldilocks spot" Avoids cruise crowds & tour busses, but easy walk to FIRA highlights, quickie bus to OIA. My bargain is just feet off the caldera view, lovely family-run place, breakfast, free transp to ferry AND use of next-door Pool!! VILLA FOTINI - https://santorinivilla.com This AM it shows several "doubles" available for June 12-14 (some w. double bed, but the girls could share). It only has about 10 rooms, so feel OK with daughters next room. Rates about $70-80 - but the pool use is GOLD. Contact NOW & say janet from Philadelphia sent you! IF you miss out, a Fallback is the pool hotel, https://www.hotelmargarita.gr a bit farther from rimside View, but also a bit lower rates.
NAXOS - ST GEORGE/Ag. Giorgios Beach - Beach directly adjacent to Port town -- check it on "skymap" http://www.skymap.gr/apps/site/viewmap/?mapid=29&cid=305 -- best of both worlds, not overcrowded, quiet at night, but a few minutes walk to town attractions. Beloved by teens -- they can safely wander into town, plus frequent bus to other beaches. NOTE: Many r Small family-run places 8-12 rms, perfectly safe to have teens in adjacent rms. Most have kitchenettes & balconies w views. Use booking.com with search terms "Agio Giorgios Beach Naxos" for Dates of June 14-19, and 2 adults/1 room (you see more choices than if you say 4 adults 2 rooms). 40+ choices: filter "lowest price first." To see location, click on a random hotel and then click "show on map" -- & do ++ to make big. U'll see ALL available hotels, WITH prices for 5 nites. for €50 per room or less (€250/5 nites) in good locations my Faves are LEFKES STUDIOS, SIGMA STUDIOS, GALAZIA STUDIOS ... Also check AEGEON, 100 yards further off beach but has pool plus a unit for 4 (twin beds & 2 sofabeds). My own gem, NOT on Booking.com, is STUDIOS NAXOS - https://www.studiosnaxos.com (on booking.com map it's next to Panormos Hotel). June rates may be going up, were about €40/double. If u email, say Janet/Philly sent you.
ATHENS -- On booking.com Put in Dates 6/19 - 6/21, Destination as "Acropolis" filter by Lowest price first. Click a hotel, then click "Show on Map" to see ALL available places AND prices. My own GEM, PHAEDRA Hotel has rooms. direct site = http://www.hotelphaedra.com Do NOT use form, send polite e-mail - say Janet sends you, explain needs. If PHAEDRA can't help, use that booking.com GoogleMap for well-located hotels or some apartments now renting thru book.com. Remember, click + repeatedly, to show all available places.
GOOD LUCK -- Book NOW - don't hold off until Mom is for sure. once u have a booking, if things change & u must "tweak" (i.e. Mom doesn't come), then hoteliers likelier to work out a change.