I've had one of the old style micras and loved it. 80% of the fun and handling of the mini with japanese reliability and five door practicality to boot. Could happily fit two mtbs on the back, all our crap in the boot and two of us on the front seats. Same with climbing stuff. Used to fit a huge weekly shop (was catering for 12-14 blokes on a full board basis) in it as well though it wasn't looking too hot on the suspension front!
Great little car, made the trip back and forth from the French alps a couple of times, good fun on the mountain roads, excellent on petrol, can fit five in for a night out if you're all good mates!
Another vote for the Panda here but personally I'd go with the old style ones if you have the option - they handle much more like a mini. New ones have done very well at keeping the handling but are still a modern car with power steering and what I feel is a high seat position - don't feel connected to the road like I do in the classic Panda or the mini.
However both of the above are getting old now so not sure if it's what you'd be looking for. But those are the two cars I would say are most like the mini to drive.