Ed brings up some interesting points about tires/shocks. I will share my experiences. Switching from Toyo to Hankook, I notice a much better ride with the Hankook. Sidewall construction is the main reason for the difference. Also, recently tried different tire pressure settings and to my surprise, I found running higher pressures in the front (105 to 115) made the ride better, not worse... On the shocks, I switched from Bilstein to Koni FSDs and they made a huge improvement in ride and handling.
BTW, you can get much better handling and ride on the Mini Cooper by replacing the "run flats" with a good high performance summer tire. Be sure you carry a can of tire puncher sealant and air pump for good measure.