A sub-$3,000 land budget can support a strong 7–12 day trip when you control the number of moves, choose mid-priced regions, and reserve lodging early enough to keep choices open. For two travelers, shared rooms help, but transport and food still scale per person.
Treat international airfare separately until you know the departure city. A plan that fits under $3,000 before long-haul flights may not fit after them, so state clearly what the cap includes.