Make sure you follow building guidelines regarding the installation of hard flooring and any requirements to provide for sound attenuation within any new floor construction.

Lots of ways to do what you want.

Heather, we are getting ready to install hardwood over concrete on our second floor. We've bought an underlayment called Elastilon and are very excited about it, but haven't started our install just yet to tell you how it's worked for us. But I have read lots of good things and can't wait! It is supposed to feel "solid" underfoot, not like a laminate or hollow sound you might get from a click-together floating floor. It is technically a floating floor, but look into it, you might like that option. If we were going to have a professional do it, there are other options such as installing a wood subfloor first (but this will build up the height of the floor and you might have problems with low ceilings or transitions into other rooms like tiled bathroom or kitchen), and some installers might even glue hardwood down to the concrete - that is not recommended by all installers, there are a lot of factors such as species, location, humidity, etc, that could affect that choice. One installer would do it for us but recommended using only "shorts" which are short pieces of hardwood.

If you plan to remove the vinyl tiles you may want to test them for asbestos. We have some vinyl tiles in the bonus room over our garage but are planning to go over them with the Elastilon because we don't want to deal with the removal with possible asbestos (house built in 1975). Good luck!

There are also engineered hardwood options with thick sliced veneer surfaces that look exactly like solid hardwood. Look into that made by Owens, for example. Owens was bought by another company, but I still think you can search under the name Owens.

These are glued down constructions...and they can possibly be installed by a floating method.

Heathermor,
I would check with my association first to see what the bylaw requires about wood floor installation, usually in form of STC and IIC rating. As far as I know, floating is the preferred method most condo approves with a high acoustical underlayment. For the actual installation, as glennsfc advised, you should be able to find really solid feeling engineered floors to float on a good underlayment. If your subfloor is sound and leveled, you should not experience much of hollowing and bouncing at all. Attached is a heavy 1/2" stranded woven bamboo floor with G5 valinge loc installed in a Minneapolis down town Highrise. If glue down and staple down methods are allowed by your association, you may consider those options too.

Thank you all for your help. As my offer has not yet been accepted on this apartment I continue to daydream about my new floors. My understanding is as long as I hire a licensed and insured contractor or do it myself and meet building code I can do whatever I want. My preference is for a long lasting floor that will not need refinishing in the next ten years. I love finished in place hardwood, however I don't know if I can afford that. For now it is all a dream anyway. Again thank you all and I will look into any suggestions made.