I've never stayed along I-drive, but the Convention Center is much closer to US. You should be able to easily take the I-Ride trolley from the most of the properties near the convention center to Universal Studios.
I doubt that any of those properties are going to have complimentary transportation to WDW... just like the Kissimmee hotels don't offer complimentary to US.
The shuttles for hire will normally make stops at multiple hotels, so it could take you a long time to get to WDW. You might want to consider renting a car on the days you go to WDW if there's more than 2 of you heading to the parks. R/T from convention center to WDW will be around $15 per person per day. So if you have more than two people heading to WDW, it is more cost effective to rent a car.
The Peabody looks beautiful, I would imagine that you would have an enjoyable stay there.
Good luck!
Lisa