This is what I think(In my opinion) a future Earth ship will look like.
It will be more oval than round, with visible weapons on top and a shuttle bay on the bottom. It will have many antennas in different spots on top mostly and some on the bottom. There will be some windows, one for the bridge, and the rest for places like lounges and control centers. There would be extended bulges on the sides, where huge solar sails come out for inter-solar system travel takes place. for between solar systems the ship would have an FLT drive similar to Warp Drive.
Inside the ship you may see square hallways at least 8' tall and 7' wide, with titanium doors that come down in-case of a hull breach. I think the crew quarters will be like ST Enterprise. Young cadets share rooms, while officer have their own. There would at least be 2 fusion generators(one in front-one in back), with batteries for emergency power. My guess is that by then, scientist will have some sort of material that creates a small gravitational field(maybe some sort of new metal-materials). The ship will amplify this field with electricity. The bridge from on top will be concealed. There might be some kind of regenerative skin on the outside of the hull and on the inside.
This ship will be built near the asteroid fields between mars and Jupiter, along with its sister ships. I think the dock yard and the crew will be international.
The ship will be At least(little bit bigger) the size of ST enterprise NX. length wise. It wil be at least 15 decks tall, each deck in 10' tall(it includes the crawl spaces where heating, air, pipes, and electricity transfer conduits), and 7 wide. (this doesn't include science labs, quarters, et. Thats just the measurement of the hallways)