We stayed at Mercure Yokosuka for seven nights while visiting my mom's family, and my wife's son who was working at the navy base.
The hotel is just a few minutes walk from the Yokosuka Shiori train station, which we used a number of times to do some sight seeing.
Right across the street, via an overpass that crossed over the main road, was the Coaska shopping mall, which we visited a number of times for groceries, coffee, dinner (Sushiro was a favorite) and just plain old curiosity.
There's is a Tully's in the mall which has some of the best drip coffee I've had in a long time. The staff at this coffee shop was so polite and helpful. A definite shout out to the woman who I talked to a few times who spoke fluent English. She is Japanese, and had moved back to Japan about a year ago after living in Los Angeles for about 20 years (if I remember correctly). It was delightful to talk to her and get to know her. I'm sure I'm going to get this wrong, but I think her name was Eko - my sincere apologies if I get that wrong.
The Starbucks that was on the Coaska property (in a stand alone building) was also great. Also, they open earlier than Tully's (0700 vs. 0800).
Speaking of employees/staff, I must say that the staff at Mercure Yokosuka are incredible. Wonderfully helpful, attentive, polite and very aware of everything that was happening in their lobby. I enjoyed my interactions with every one of them. Many, many thanks for making our stay so enjoyable.