Well, that was fun
Prime Directive travel speeds are much higher than in core d20 Future rules. Warp Drive is a Progress Level 7 technology.
Warp speed was recalibrated to a 1-10 scale (with 10 being infinite speed) between TOS and TNG. This system uses the older TOS scale which has no upper limit. Note that speeds above Warp 10 on this scale are known as “transwarp speeds”; during the TOS era, only the USS Excelsior possesses an experimental transwarp drive. These become much more common later.
1 parsec = 3.26 light years = 1 hex
This turns out to make Warp 7 very close to 1 day per light year, making it standard travel speed for long-range journeys. With local variations and other factors taken into account, it's safe to say that Warp 7 is 1 day per light year.
On the main galactic map, 1 hex is one parsec. Therefore travel from Earth to Vulcan (4 hexes) takes 3.47 days at Warp 7. See this article on the size of the Federation; this page supports the "small Federation" theory of a few hundred light years diameter.