I can't think of any poorly nucleophylic strong bases.
I can't think of any good nucleophiles that are only very weakly basic.
I guess that answers my question.
Unfortunately not, think again!
Example of a poorly nucleophilic strong base: LDA
Example of a good nucleophile that is a weak base: iodide
See if you can think of others.
Nucleophilicity does not necessarily parallel basicity, other factors such as polarisability and sterics are important.