First-time trip to Thailand - Koh Samui and Chiang Mai?

I’m thinking of travelling to Thailand this summer for about 6 days and was considering splitting my time between Koh Samui and Chiang Mai.

I’d like a mix of adventure, scenery, culture and a bit of luxury, but I’m not really interested in nightlife or heavy drinking.

Would this combination work well for a short trip, or would you recommend other locations?