Depends how much you are prepared to spend and what you want from a tyre.
The fact that you used "tyre" I guess you are in the UK
The best tyres are the Michelin XAS FF 165 HR 13. These are the original design that would have been fitted. However they are now made using modern processes and compound, the same compound as the Pilot Cup tyre. Very sticky but will not last long.
Another option is to go up a size to 185x70x13 where there is a greater choice. However even with this size you are still not in to the high performance tyres you need to go to 185x60x14 to start getting in to the main stream performance models.
FWIW I use the Michelin XAS on my baby Elan (155 HR 13) and I am very pleased with them. Modern levels of grip but maintaining the classic neutral handling.