Not unless there have been some spectacular overnight improvements It's about 50 minutes. The services are reasonably comfortable and extremely frequent - every 15 minutes during the day.

The Holyrood (directly opposite my office, as it happens) is a good choice if you get a nice deal. The accommodations are good and it is in the Old Town, right next door to the new Parliament and behind the Canongate/Royal Mile but it is a little bit further away from the action than you might expect. Somehow, being at the bottom of the hill makes the distance seem further

The Tower restaurant is on top of the excellent National Museum of Scotland (so not really off the tourist path, but still excellent) and is owned by the same award-winning restauranteur responsible for The Witchery by The Castle which is a great place for a blow-out romantic evening dinner on a cold night. You'll need to book early for both venues. Henderson's is veggie (but still nice!) but there is also an excellent restaurant a few doors down called Fishers in the City with great local seafood.

Jury's Inn, Apex and Holyrood are, in order, the nearest fit for your Old Town requirements...but may I ask why the preference?