Need some suggestions

I went to the Steinway store where they have an auditorium behind the showroom with two 7-foot Model B's side by side that the college students get to use for recitals on weekends for no cost, and customers can go back there and play these whenever they like so long as they are not reserved for recitals.

I went back and played on both of them to see if they were in tune and how well they sounded to my ears, and they are both good, one slightly better than the other.
 
Then I returned to the front of the store and spoke with the lady at the desk and also one of the main salesmen (whom I have spoken with a couple of times over the years) and I asked if it would be possible for me to bring my computer and a couple of microphones into their auditorium on a weekday in a month or two (I need time to practice), and record myself for a couple of hours.  The lady said "sure, just give her a call before I go up there so she can verify that the room is vacant.” 
 
I'm kinda up about it, but here's the problem --  I'm really not a recording engineer, I lack the important mics, and also the following:
 
My desktop system is far superior to my laptop, but very cumbersome.
A big Mid-Tower desktop PC (i7 4790K 4.0 GHz with 32GB RAM and SSD drives), a Monitor, keyboard, Mouse, Mackie CFX-12 channel Mixer, some cables, and I only have one mic stand with a boom arm.  And the wrong type of mics.  I have a Sure SM-57 and a condenser EV BK-1 designed for singing from any direction.

I also have Lenovo Laptop X230 (i5 3380 2.9 GHz with 8GB Ram and SSD drive) that should be able to do the recording (I have Sonar X3 Producer and all my plug-ins installed on it as well), but it's way less capable CPU wise and ¼ as much RAM as my desktop.  But this would be far less cumbersome, and it might be sufficient to record piano with a couple of mics?  I own a small Alesis MultiMix 4-channel USB mixer that I would use with my laptop.  Sound quality probably not great.

Admittedly, I have not tried setting up the laptop to see for myself how well it might sound.  I can experiment with my console piano here at home.
 
'Don't know what to do.  I don't know anybody here in St. Louis to help me. 
 
Then there's a part of me that thinks I should just download several trial piano samples (Ivory, etc.,) and see if they would sound acceptable to me, and I would be able to record and make infinite numbers of MIDI edits to get the "recording" perfect, but I know there's no comparison to the sound of a real piano recording (one with a bright sound), with that live energy in the performance.
 
Perhaps I could rent a couple of proper mics and do it with the laptop?  Where should mics be placed?
 
Suggestions?

Cactus Music
The computer is not that important as far as recording audio goes. I record 16 tracks of Audio to my 2008 Sony laptop. What is important is the mikes, placement and of course a decent audio interface. But!  
 
My self I would just use my Tascam DR40 which has amazing sound quality. They have a camera tripod mount so you can experiment with different placements. Talk about easy. I cannot say enough about how many uses I have found for it. I record every gig I do. I also keep it handy for song ideas. 

 
Really.?.  I remember when those things were first introduced.  I never gave them much of a look-see being a keyboard/synthesist player and having all my gear fed directly into a PA system.  But now, perhaps there is a reason to consider.