If you really want do Trek & at the same time avoid long drives I would suggest places near Kathmandu Valley It closed to Kathmandu
Total relaxing Tour & you also get to see beautiful landscapes of Himalayas
Great viewpoint near Kathmandu. Stay at paradise lodge or Guest there are many different type guest house depend on you budgets enjoy great cuisine with beautiful view of Nagarkot.
Great thing about being at Nagarkot is 360 views of the Himalayas, probably best view near Kathmandu. Nagarkot View Tower is stunning.
Additionally, you get to be at Rara National Park which is one of the finest National Parks in the world sheltering native musk deer & Himalayan black bear.
Chitwan National Park can be the good option for you. At Chitwan national park take elephant safari, elephant ride & bath. Its early summer now you can get most out form National Park.
These are my Top 3 Recommendation for you However I need to mention some good treks other than these:
4.Annapurna Panorama Trek, Helambu Trek, khopra Danda Trek/ Langtang Valley/ Tamang Heritage Trek /Mahore danda Trekking / Kathmandu valley Trek- Bardia –Lumbini and Pokhara /
Good luck Nepal Nepal Trekking and Travelling Hope you will find the information useful.