If you love castles and forts then you are in the right place! Chateau Chillon is in Montreux and is one of the more picturesque castles in Europe in my opinion! It sits right at the edge of the lake and is beautifully preserved. If you head east to the valley of Valais, 30 minutes east of Montreux, it is dotted with many castles in various stages of repair and ruin. My favorites are in Saillon and Sion. Saillon is a tiny village that is extremely cute and you'll have the ruined castle to yourself. The town has constructed a steel staircase in the remaining tower and you can climb to the top and enjoy the amazing view of the vineyards in this area. If you drive further east up the valley, the town of Sion has the fantastic Chateau de Tourbillon perched on a hilltop in the middle of town...half of it is a ruin and the other half, where the chapel is, is in pretty good shape. There are murals that have been uncovered recently that date to the 1300s - they are as bright as the day they were painted. The other small hilltop right adjacent to the castle has an ancient church that dates to about the same time the murals were painted. It has never undergone any kind of updating or restoration so it is very unique inside as European churches go. It has the oldest working pipe organ in Europe.
Another place you might enjoy is Gruyere, about 40 minutes north of Montreux/Vevey. Obviously, you go for the cheese, but there is alsocute nice medieval village of Gruyere on a hilltop with a small chateau that is really lovely...a little touristy but still worth a visit.
It sounds like you might be into walking since you love nature? In Valais there are many bisses, hand dug waterways that are very old (some as old as 800 years) that were created to bring water from the mountains to the orchards and vineyards in the valley below. Some of them are at lower elevations and have hiking trails next to them...some have spectacular views! Not sure if this will word in May but it's another nice thing to do to get out and enjoy Switzerland.