Shoptalk has lots of maintenance stuff. If it's gas is over 2 months old, DRAIN IT. Put a gallon of some fresh gas in and drain the fresh gas through the bottom of the floats. Then fill tank halfway and pour a bottle of Techron in it, and hope the jets haven't clogged. Then cross your fingers, and push the start button...
If the bike is already running, my preferred method of draining the tank is by riding to the mountains and back.

Priorities for a newly purchased Valkyrie:
1. Oil change unless it's known it was changed this riding season AND less than XXXX miles since last change.
2. Check the air filter and replace if required.
3. Coolant change unless you know it's been changed within the last year or two.
4. If brake & clutch fluids look dark, change. If not bad, wait until next front brake pad change and then change front & rear brake fluids and clutch fluid.
5. At next rear tire change, thoroughly clean rear wheel drive splines & drive shaft splines and reapply appropriate lubricants. Also change final drive gear oil. Any time your wheels are off, inspect wheel bearings for smoothness.
6. At your leisure, but certainly within the next year, clean and re-lubricate starter button (requires disassembly) and turn signal switch.
7. Sometime within the next two years, get the valves adjusted and the carbs synchronized. If the engine is running rough, do this sooner.
Other (in no particular order):
1. Check the tires for the manufactured date. If they are more than 5 years old, seriously consider replacing them regardless of remaining tread as rubber hardens with time.
2. OEM Valkyrie batteries tend to last 3-7 years.
3. Some parts to have on hand because it's hard to predict when you might need them, and you can't ride until they're replaced or Macgyvered:
Side stand spring and side stand spring retention bolt.
Throttle cables.
Wheel bearings and associated seals.
U-joint.
Fuel valve cover set (repair kit for vacuum operation of fuel valve).