The Engadin could work at this time of the year. Start out in Maloja and hike down the valley towards Scuol. Due to the snow at higher elevations you will have to stay down in the valley. Guarda would be a must see place and a good starting point to visit different parts of the Engadin. Relatives enjoyed Pension Val Tuoi http://www.pensionvaltuoi.ch/ I spent many weeks of free 'holidays' in the Engadin with the Swiss army. May was usually quite nice, with the valley floor turning green and white mountain peaks standing out against the blue sky (I had a lot of time to study the scenery )