I rode my WR-250R as a street-only bike last season, from March until September.
I used the stock Bridgestone tires it came with.
I rode the bike as if it were a light-weight sport bike, railing corners and having fun on back roads.
When they wore out, I got more of the same.
I felt they performed very well and gave the bike a good feel.
I think it you demand even more grip, you'll be looking for something that's basically a street-only tire. :)