I did the calculations for Enterprise quite some time ago so I don't have the exact numbers in front of me. IIRC, I worked backwards from a volume similar to the Ambassdor class (about 2.8 million cubic meters) and the space shuttle's basic density (about 100kg per cubic meter). So if we built a ship the size of Enterprise with TODAYS space technology, it would weigh something like 280,000 tons. Then I accounted for the use of much lighter materials in the ship's construction -- closed-cell metal foams, metallic glasses, advanced ceramics, etc -- and reduced that weight by a third. The older flagships and the more conventional ships have slightly higher densities, but they're also a bit smaller.
Still, the fully-loaded Enterprise, with a standard mission load of equipment, fuel, food, shuttles and crew on board, would come closer to 210,000 tons. I'm not quoting an exact "fully loaded" figure for the ship because, frankly, such a figure would be completely irrelevant for a spacecraft whose only real limitation is the volume of its cargo bay; you could fill the ship with neutronium and it could still fly (if a lot slower than usual) to the nearest starbase to deliver it.
ETA: Significantly, I found a tag reference in my notes from 2011 that a spacecraft's density actually decreases with volume, primarily because most of the mass of the ship is concentrated in the outer layers (heat shields, radiation/impact protection). An ISS module like Destiny, with a density of 120kg/cubic meter, would have a density closer to 70kg/cubic meter if you doubled its size.