About the 3rd week in May we will be arriving in Basel (River cruise ends there) and wanted to see the Berner Oberland area but that doesn't look like a good idea in May. Many hotels and restaurants are closed. Suggestions for 3-4 days in Switzerland?
In May the weather can be dicey so, in my opinion, I wouldn't make seeing the mountains your first priority. I would focus on really nice cities such as Lucerne or some of the other smaller cities and towns that are, in and of themselves, picturesque and interesting. If you get to see the mountains then that will be icing on the cake!
Hard to predict in advanced, but because this was a mild winter, the Berner Oberland may be more "hikable" then usual this May, although that won't necessarily influence the opening of the restaurants and hotels. You could consider basing yourself out of Interlaken. That would give you more flexibility for side trips to places like Bern, Thun or even Luzern, if the weather in the mountains is cloudy, but still allowing you easy access to the Alps when the sun comes out.