The Japanese have been doing this for a century or so. They have taken it to astronomical heights. Make a study of what they do. Their department stores are an absolute delight but the superior grade gift wrapping costs a lot.

Some points:

It only suits expensive or very special gifts.

There's only a few department stores that don't do it.

In the event of any downturn in the economy your business will be one of the first to take a dive.

Selling the service might be difficult, but even more difficult is finding somewhere to do it.

May I suggest some alternatives?

Sell a 'unique gift-wrapping kit' so buyers can do it themselves where ever they are in the USA.

Teach it in short courses to department store staff.

Select the finest gift-wrapping materials from all over the world and sell them wholesale and retail. Does anyone do this?

Select and sell the materials based on culture (Japanese for example), style, period (30's look for example) color of course, closing materials (the ribbons, seals, ownership markers), filler materials, and attached note materials which have to be superior just by themselves.

As for the financial angle you'd have to tell us if you want to set up in your own shop-front, as a desk at a department store, sell online (eBay too?). The method of selling determines the costs.

In any case, get yourself a spreadsheet program and develop out all the costs to set up in your chosen environment.

You can raise the money in the usual way. Go to a bank with a business plan in hand, raise it from friends/family, save it up yourself or take on a financial partner.

There's a few things to think about. Y'all come back now if you want more ideas.