So the garage has a regular 3 pin outlet (110V). Can anyone please give me a high level estimate of what the cost will be to upgrade the outlet to 240V 30Amp so I can charge my Model S at home? I understand that the cost will vary but I am looking for a high level estimate. I am in the chicago suburbs if that matters. Thanks.
As others have said, there is no way to "upgrade" your 120V outlet to 30A 240V. The 12 AWG wires that are likely there will not support more than 20A. If someone went cheap and wired with 14 AWG, then the best you can have is 15A. What you CAN do with the present wires is upgrade to either 15A 240V or 20A 240V, depending on wire size.
One complication might be that your existing outlet is one of several on the same circuit. If so, then changing one outlet to 240 may force you to make them all 240 if the one you want to covert is last in line on the branch circuit. Whatever is downstream of the converted one can still be wired 120V, but anything upstream must be blanked off or converted to 240V
Fortunately for you, Chicago electrical unions' political power made metal conduit mandatory for many years (perhaps still) so you probably have conduit going back to your service entrance panel. If it is large enough conduit, you can pull out the old wires and pull new wires big enough for your charging port:
30A 240V needs 10 AWG solid copper wires, which will fit easily inside a 3/4" conduit (a likely size for an existing 12 AWG circuit) and you can install a NEMA 14-30 dryer outlet in a new 4" box. There is a 14-30 adapter available (again) from Tesla that automatically restricts charge rate to 24A and enables you charge at 5.7kW, enough to charge my S70 from 10% SOC to 90% SOC in about 9 hours.
50A 240 needs minimum 8 AWG THHN copper wires and that would be a snug fit in 3/4" conduit; doable if there are no tight bends and not too many 90º bends altogether, and with a lot of wire-pulling lube. That would have you charging at 9.6 kW, capable of charging my S70 from 10% SOC to 90% SOC in about 5 hours.
Of course, if the panel is in, or near to, the garage, a whole new conduit could be pulled to your desired charging outlet location.