Plane, Trains and Automobiles?
Swindon is home of the MINI, and the Mini-Roundabout so
From M4 Junction 15 Badbury Roundabout [ this is a biggie] , take the 2nd exit onto Marlborough Rd/A419 NORTH signposted to CIRENCESTER and M5 Gloucester
Approx 1/4 mile take the slip road signposted to A4259 Swindon and Great Western Hospital.
Follow for approx 1 mile, go passed the Hospital and the new houses... until you reach the SUN INN roundabout at Coate Water [ the Sun Inn will be on your left] take the 1st exit [ another biggie] signposted to OLD TOWN and Wroughton. [If you have half an hour Coate Water is a lovely walk around the lake. Full of Autumn colour at this time of year and misty vistas across the water to Badbury Hill, where the last battle for Wessex took place.]
Go across 1 mini roundabout [this is one of the 186 minis in Swindon] and bear Right [grr] and the 2nd - following signs to Wroughton.
At the next roundabout [biggie] go straight across[ another mini] - you will see INTEL slightly to your left and the Marriott dead ahead.
From Junction 16 - to be honest unless you like roundabouts [and I mean a lot of roundabouts] I would stay on the M4 and come off at Junction 15! It's a little further BUT a whole lot of roundabouts simpler.....
Sat NAV - please use postcode SN3 1SH, the address is Marriott Hotel, Piper's Way, Swindon, Wiltshire.