Help with itinerary for anniversary trip

Celebrating 5 year anniversary in Greece in early June. Flying into Athens and overall will have 13 days total. We are thinking of spending the first day and last 2-3 days in Athens, then spending the remaining middle 10-11 days split between 2-3 islands. Which islands would you recommend spending 3-4 days ish at a time? Thinking of Naxos, Santorini, maybe Milos? Mykonos? We want lots of beach days and time by the water (more chill relax vs party vibe) and would also love a cool hike one day and any local art markets and shopping. Don’t really care about crazy night life, but we are night owls and would stay out at a more cozy casual patio vibe bar. Would prefer to rely on public transportation or scooter or bike rentals and we also like waking a lot. Trying to keep it around 6-7k (excluding flights). Any suggestions?