There is no such thing as a minimum dimension for the riders height. It purely depends what you find comfortable. Sportsbikes (eg Ducati 1098, Suzuki GSX-R etc) are cramped for just about everyone but great fun, cruisers (eg many Harleys, Yamaha Virago etc) offer a more laid back riding position that allow you to stretch a little and often have a low seat height but great fun, standard/traditional road bikes (eg Honda Hornet, Yamaha Fazer etc) offer something in between and come in all engine and frame sizes but great fun, dual purpose tourers/adventure (eg BMW GS series, KTM ADventure, Moto Guzzi Stelvio etc) tend to be phyiscally bigger bikes with taller seat heights available but great fun.
I assume you can see a common thread here.
If you want to decide purely on something that will have the physical characteristics most likely to be compatible with your height then the BMW GS, KTM (most models), Yamaha Tenere, Honda Varadero, Moto Guzzi Stelvio, Suzuki V Strom, Triumph Tiger and similar direction may be a good starting point. Also consider the big tourer Honda Gold WIng, Harley Glide, big BMW option.
I personally would not rule anything out until I tried a good mix of what appealed to me for other reasons. You could be comfortable on any kind of bike if you enjoy it enough.
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