Open ended amount of time?
If so, my response would generally include my home country and two countries I haven't been but seem intriguing.
The home country since this is where I have most connection with people, language, culture and chance to connect on bicycle. At present this is USA and I've cycled in all 50 states, but if my home country were somewhere else than that would be my answer. I am a big fan of Canadians riding across their country, Australians seeing more of Oz, Indians exploring their country, etc.
Beyond the home country answer, one that has been on my intriguing list for a while is the Pamir Highway through Kyrgyzstan. A combination of the raw beauty, challenge and less developed aspects put this on the list. If I could cheat on your rules and get to my start cycling through a few other central Asian countries
that would be bonus too.
The other one on my intriguing list would be northern India, particularly Rajasthan and Kashmir. I've been to southern India but not the north and mixing the classic Taj Mahal visit with some desert cycling and Himalayan foothills is intriguing. Again if I could get to my starting point by cycling across China/Tibet and Nepal even better