This could go many ways, depending on whether you mean a clean sheet design or incremental updates to STS. I'll assume the latter, in a parallel universe where the STS-107 accident never happened and the program continued on and actually did upgrades.
We can look at what was planned for STS:
- Improved engines: health monitoring, new controller, new nozzle and combustion chamber design
- Electric power for the hydraulic pumps instead of toxic and dangerous hydrazine APUs
- New avionics and cockpit controls & displays
- Blowdown-type thrust vector control system for the SRBs instead of toxic and dangerous hydrazine APUs.
Other, more expensive and/or speculative updates
- Liquid fueled fully reusable flyback boosters
- Metallic or otherwise hardened Thermal Protection System
- Operational improvements to reduce cost - reflying crews as a unit to reduce training, for example
- Forward-to-aft Reaction Control System interconnect
- Revisit and fully implement the Extended Duration Orbiter project (cryo pallets, Orbital Maneuvering System kits, regenerative CO2 removal, new toilet)
- Add Shuttle-C-like vehicle as an option for heavy lift missions where crew is not required
- Crew escape system - via separable crew module?
The second link leads to an entire book titled Upgrading the Space Shuttle which may be of interest. I have only pulled a few items from it.