The easiest cool-weather escape is Pyin U Lwin (still widely known by its colonial name, Maymyo), a hill station about 70 km east of Mandalay. It is a town of Nepalese and Indian families, famous for its sweater knitting and its fruit, where horse-drawn pony wagons still rattle along the streets. The British-era National Kandawgyi Botanical Gardens are the main draw — a relaxing half-day among well-kept lawns and a fine orchid collection, with views from the Nan Myint Tower. To get there, take a pick-up truck from Mandalay's central bus station.
From Pyin U Lwin you can carry on by road or rail to Hsipaw, and even as far as Lashio, without a special permit — but always check current requirements with MTT before you set out, as areas beyond this point may need one.
From the central bus station you can also take a minibus south toward Inle Lake, a long but rewarding journey through the Shan Hills. On the way you pass the hill station of Kalaw, where you can get off to walk some of the region's best trekking trails before continuing on to the lake.