If you don't own the Imperial City DLC, you cannot enter the Imperial City. I'm a little surprised that you can pick up the quest without owning the DLC, but I suppose its ZOS subtly hinting that you should get it?

If you aren't planning to buy the DLC, just abandon the quest. If you do get the DLC, you'll get access to the Imperial City, a PVE/PVP questing zone, the ability to farm Tel Var stones to purchase gear and variosu other items, two new dungeons, and a fair bit more. Do know that the Imperial City often has a low population of players, since not many PVE players enjoy getting ganked in the middle of questing/tel var farming, but for some people the risk/reward factor is the best thing about Imperial City. The Dungeons are mechanics intensive as are most DLC dungeons, but they are also very fun and rewarding.

Edited for spelling: Imperial City often has a low population, not a long population.