Buses to Masvingo leave when full from Harare's Mbare bus station, cost about $7 and take about five hours. You can also potentially get one of the "luxury" buses between Johannesburg and Harare's Roadport to drop you off, but this will be much more expensive and is unlikely to work in the other direction. Minibuses to/from Bulawayo cost about $8 and take 4.5 to 5 hours. In Masvingo, transport to/from both Harare and Bulawayo arrives/departs from Bradburn Street, on the western edge of the city centre (marked on Google Maps). There are also buses/minibuses towards Mutare.
The town is sufficiently small enough you can get around on foot.
The Great Zimbabwe ruins are about 25km south of town.
Not much available apart from Chicken Inn and Pizza Inn. You may also eat at the Victoria Hotel restaurant.
The stone ruins of Great Zimbabwe are about 25km south of the city. You can get a combi from behind the TM supermarket just south of the town centre, costing around $1 and taking around 20-30 minutes. This will drop you about 2km from the gate to the ruins. Taking a taxi is also possible but much more expensive.