The Speed Demon thing was easy for me. My effort was with the McLaren F1 GT Base Model car around the Daytona oval. I plan on getting a Bugatti Veyron to race around Special Stage Route X or Special Stage Route 7 (which I used to get a similar Trophy in GT5). Keep the Veyron stock. She'll reach that 240+ mark easily as long as it's on a track with very long straights. The car might even reach that crazy top speed at Circuit de la Sarthe (without chicanes).
You have some options, but it shouldn't be too difficult to get either Trophy.
Speed Demon: I think it was in a Mitsubishi GTO Twin Turbo MR.
111m/sec: Alpha Romeo TZ3 Stradale. I've had it up to 558km/h bump drafting online at RouteX.