There are dozens and dozens of museums in and around paris: le musée du Louvres, Le musée d'Orsay, le Centre Pompidou, le musée du Judaïsme, le musée Picasso, le musée Cluny, le musée d'Archéologie Nationale, etc. There are more than a hundred in Paris and probably as many in the rest of Île-de-France, not including all the monuments and "interesting" locations like famous artist' homes and so on… so that's easily enough for two years worth of culturally-oriented week-ends.
If you have a bicycle, you can ride along the canal de L'Ourcq or the canal St Denis, in the North-East or maybe take the Coulée Verte in the South-West. Many parts of the banks of the Seine are really nice for bicycle rides, mostly outside of Paris and mostly under-advertised.
If you want some fresh air, the amazing (IMO) Forêt de Fontainebleau is about 20 minutes of RER away. There's also the Forêt de Rambouillet… and plenty of others.
Summer is festival season: the La Défense Jazz Festival, the Paris Jazz Festival in the very nice Parc Floral, Solidays, We Love Green, Villette Sonique, Rock-enSeine, etc…
Tech-wise, there's BestOfWeb on the 6-7 June and of course lots of meetups. You will have to reach out to your particular communities to find out the times and locations or google it.
