You would want it at the top of the house if it’s purely for cooling. Cool air at the top of the house will sink down to the bottom. Rising hot air will then be cooled by the A/C unit. If you put it at the bottom, all that cool air will just sit there and never move upstairs. The open window upstairs will allow hot air out… if it’s cooler outside than inside, otherwise it will allow hot air in. In either case, that won’t promote much mixing of the upstairs and downstairs air, so your A/C won’t improve the temperature upstairs much.
You would want it at the top of the house if it’s purely for cooling. Cool air at the top of the house will sink down to the bottom. Rising hot air will then be cooled by the A/C unit. If you put it at the bottom, all that cool air will just sit there and never move upstairs. The open window upstairs will allow hot air out… if it’s cooler outside than inside, otherwise it will allow hot air in. In either case, that won’t promote much mixing of the upstairs and downstairs air, so your A/C won’t improve the temperature upstairs much.