I haven't slipped in HRE since beach fleet days, but the nearest decent lodge then ('97) was Pamuzinda, 45mins drive - they'll pick you up. The Sheraton will have the no.
If you get 2 clear days Vic Falls is doable but a long long ride if you don't go by air.
Zimbabwe balloon flights would pick you up at the Sheraton (bloody early!). A great day but pricey.
Finally, if you contact Mashonaland flying club at Charles Prince airport they will be only too glad to see you. I guess they struggle to get petrol there now but a flight to Bumi Hills or Kariba is easily arranged and a brilliant day out, the best of all these options.
I really miss HRE.........hope you can arrange something next time you go.
Sad waste of a country.