Oh I am so jealous! I love, love, love Crete and you are lucky you are flying to Chania not Heraklion. We have lots of Greek extended family and have been travelling all over Greece and Southern Crete is one of my favorite places.
Greece is my speciality subject :)
Ok. First of all you will need a car as Greek public transport is as useful as a chocolate teapot.
My favorite place is a tiny village called Sougia, they have their own website. About 1.5 hr drive from Chania. It's not whitewashed houses Greece, just a tiny village community! It's kind of isolated, near a national park, spectacular mountain scenery. Not crowded. This is very laid back Greece, has a sort of hippy relaxed vibe. Leftist Greek students camp there on weekends so it gets a bit messy and the beach looks like Glastonbury but if you can overlook that the place is worth a visit. It's where Chania Greeks go for seafood and a break by the beach. Long beach with sand and some pebbles, never crowded. The village has lovely tavernas (Anchorage stands out), lots of rooms to rent, right on the waterfront. Also a lovely guesthouse available via Airbnb.
Nothing to do there though - but DH and I loved it - no noisy tourists, hawkers etc. Close to some great day trips and hikes.
It's close to Elafonissi, a truly spectacular beach (pink sand - looks like the Caribbean) with really shallow water. Elafonissi is protected by the EU, gets crowded and nowhere nearby to stay.
This part of Crete is mountainous, a little wild, not built up and very quiet. Oh it makes me want to go there again!