If the staying outside clause is due only to your allergies, then a sphynx or rex could be an indoor cat... they may not set off your allergies at all. Best to visit a breeder beforehand to check though.

Otherwise - and this is my personal opinion - cats should ideally be kept as wholly indoor pets whenever possible, for their own safety (traffic/poison/bigger predators/theft/disease) as well as for the safety of the local native wildlife. *off soapbox*