What to offer will depend on the difference in current price between indoor and outdoor spaces in your building.
As a fellow Chicagoan, I would MUCH rather have an indoor space (because nobody likes scraping ice off their windshield in subzero weather); however, the actual value of the unit will not be greatly affected. Instead, the **perceived** value will be boosted, and this is the key with resale. As suggested below, you should fish with the seller a bit to see if this is something he would even consider, since perceived value is what sells real estate, and that of his unit would be reduced.
Then again, the opposite could happen with your unit. Be sure that your and the seller's units are of comparable value so that swapping won't negatively affect the "purchase-ability" of your unit. Make sure that when packaged together, it still appears to be a good buyi. Also keep in mind that because it is a deeded spot, there are taxes adn assessments on the spot. Are they included in your assessments? If so, they may go up.
As for transaction costs, this is a real estate transaction like any other. A contract will have to be written up with the details of the purchase. You can choose to hire an attorney who may just charge you a reduced flat fee since the transaction is less complicated than with regular property, and he can write up the agreement for you. I used to be a real estate paralegal and was surprised to see how LONG the legal descriptions can be for a lil' ol' parking space.
If the space is for sale, contact an agent to do a market analysis of properties with indoor vs outdoor parking and base your offer on this information. Seek legal advise on the closing cost and transfer.
Indoor parking is advantageous in selling property,especially with parking problems in the city.
There is actual value (an appraisals value) and their is emotional value for buyers so I would say that it would probably take more than $10,000 for you to buy the space from the other seller because you would be removing one of his best selling points. It would add value to your unit and make it easier to sell. Make an offer and see where it goes in negotiations. I have seen parking spaces go for $25,000 and more here in Georgia... that does not mean it raised the properties value by that much.
If you are paying cash for the spot than the only cost involved is having a title company or attorney transfer title... should not be much especially if you give repeat business to the company that closed your purchase.
Let us know what happens!