what PSI should my Yokohama 205's be for my 18 inch rims be? I usually drive by myself, so no extra added weight...

 

Same as for 15", 16" and 17" rims.

Rim size has nothing to do with tire pressure.

Check your driver side door jam for the sticker on tire pressures which are recommended for your MINI.

You can run a little higher and check it when cold in the morning and not in the full sun.

Front and back about 33 to 37 psi is a good place to start.

Lower pressures are more comfortable on ride and grippy but have higher rolling resistance and lower mpg if you care.

18" wheels usually require lower sidewalls and have a rougher ride so slightly less pressure tends to work. Try 33-34 psi then adjust for wear.

Make sure you check alignment at least yearly or when adding new tires.
Set to OEM spec is fine for street use.