Tell me, please

[pia] Both are technically correct, and how you use each term will depend on your interpretation of George Orwell's "Politics and the English language".  (Look it up, it's a great read!).  You can write, "I went to lunch with my colleague" or "I went to lunch with a colleague of mine", and both do the job, so to speak.  It really depends on context, if you want simple, direct language, use the first. 

I feel like seeing the city. What means "feel like seeing" in this sentence?

[pia] I would like to go visit the city.  I feel like = What I really want to do, and "seeing" = to visit, to experience. You can also use see to refer to people, "Go see your colleague and find out what she has to say" for example.

Hope this helps!