Passing through

Stop in Saint Augustine and take the time to drive over to the historic part of town. It's only 20 minutes off I-95. Then, if you want something sweet & delicious, stop at Crème de la Cocoa, a dessert shop by a Food Network pastry chef. It's incredible! I'm sure there is a Kimpton Inn around there as well.

The halfway point between Miami Beach and Greenville is around Saint Marys and there is a pet friendly hotel (Riverview Hotel) there (they have cats) but it isn't a big fancy hotel - it's kind of old.  There is a restaurant there and there are lots of other places to eat in town - it is a nice historic small town but it is a little way off the interstate.  You could also go farther north to Brunswick or Kingsland or south at Fernandina Beach.  The most reasonable three star place that I found on the direct route in this area which is pet friendly (for an extra fee) was the Hawthorn Suites by Wyndham Kingsland but they charge $35 per pet per night.  I have not stayed there, but I have stayed in the Hampton Inn in Hampton Inn Amelia Island also is pet friendly for a pet of less than 25 lbs and the require a $50 deposit.  

The Residence Inn is quite a way out on the beach - I haven't eaten in any restaurants out there.  Mostly when we visit we eat in town.  Most recently we ate at Timoti's which is very casual and is only open until 8 pm on weekdays and Saturday.  Have also eaten at Bretts (nice views) and the Marina Restaurant which is in an old historic building.  My sister and brother-in-law took us out to Kabuki Japanese Steakhouse & Sushi which is closer to where you are staying but they like sushi better than we do.