what kind of bike should I get?

I started riding a bike 8 years ago.  I was 43 then and had gained
weight after quitting cigarettes.  I found a 70's 10 speed at a garage
sale.  Over the years, I increased my daily rides from 6 miles per day
to 17 miles.  I bought vintage Italian bikes from eBay and fixed them
up with the help of this group. 

As I aged I grew tired of the "racing" position so a year ago I put a
very tall techtronic stem, moustache handlebars and a Brooks
Professional saddle on my Guerciotti.  It's still a very fun ride, and
I enjoy the upright position.  I still ride it 17 miles per day.

My inlaws live in Piedmont Alabama next to the Chief Ladiga bike
trail.  This trail is described as "relatively flat" with a little bit
of gravel.  I live in Florida where the roads are "absolutely flat"
and haven't ridden a bike on a hill - ever.  I've never ridden on
gravel either.

I'll  visit this area about once every couple of years.  I'd like to
buy an inexpensive, but durable bike that I can keep up there.  As
I'll be on vacation, I'd like to increase my daily mileage or burn
more calories.  I'd like to be comfortable doing so.

What sort of bike should I look for?