Hmm, you don't really seem to have a perfect solution. Ideally a thermostat should be:
1. Not on an outside wall (especially in older properties without cavity insulation)
2. In a room without another heat source (ie gas fire, kitchen, lots of electrical equipment etc.,)
3. Ideally not in a room subject to direct sunlight. A north facing shady room is best, so the other rooms heat up first and are controlled by their own TRV's before the thermostat turns off the heating system.
4. Away from draughts.
5. In a room with a radiator (sounds silly I know, but I've seen thermostats in internal passages or hallways without radiators in. If the doors are closed the rest of the house is warm but the thermostat doesn't switch off because no heat reaches it) The radiator in the same room as the thermostat mustn't have a TRV
Regarding the places that were suggested to you:
* bottom of stairs, but within the front room - Possible, but will be effected by the gas fire if you use it.
* bottom of stairs but on the wall by the bannister (within the stairwell) If the stairs are enclosed and don't have a radiator this is not a good idea (see 5 above)
* top of the landing (by bathroom and spare room doors) If it's an internal landing, heat may become trapped as it rises and turns off the heating when it could still be cold downstairs.
* top of the stairs in the main bedroom (on the top floor's light switch) - If this is the gaming room not a good idea if there's a lot of heat generating equipment.
Personally I would go with locating it in the front room and avoid using the gas fire if the heating was on.