At warp 7 it will take 9-11 days to get to vulcan from earth (depending on sources) so im going to say 10 days for this trip unless the captain or GM decide we should go faster than cruising speed.

Warp 7 = 9-11 days
warp 8 = 6-7 days
warp 9 = 4-5 days (which we can't do)

for comparison, if anyone is interested, The USS Enterprise E can sustain it's max speed of Warp 9.99 for 36 hours and can do the Earth-Vulcan trip in between 18 and 21 hours.