You will stay on 138E all the way in to Newport. 138E will join US1N for a little while, just before the first of the two bridges.

When you go over the second bridge, stay on the freeway until it ends, and turn left onto Miantonomi Ave. (It is a left, and you will still be heading east, and you will still be on 138) When you cross Broadway 138 will go left, but you will stay on Miantonomi (ie you will go straight through.) Miantonomi will soon change in to Green End Ave. Stay on this, the ground is on Green End, just over Third Beach Rd.

(Here is a pulled back view of the transition from the bridge to Miantonomi Ave.)
 

To get to the West Main Lodge Hotel, check westmainlodge.com