if not a Morgan I would look at an MG Midget (a mate has one which is just the nuts) or more likely a Mazda MX5 Mk1 Rocketeer V6 conversion.
The reason is that I use the Morgan for days out and for road trips. The Mazda is a great car and with extra torque and power it would work very well in that role. The handling and performance would help keep one involved!
I am off on a boys road trip to the Black Forest in the Caterham next week but could see the Maxda being a more practical alternative to the Caterham. It would be good on the track day on the way home and, more importantly, eat the miles on the Autobahn.
That does not mean I would turn my nose up at a super car, budgets do not stretch to a new one, but as a special car the Cayman GTS appeals.
It would be difficult to beat the madness/fun/handling/rapidity of a caterham and they look old fashioned as well as long as its not raining too much !