It depends on how "nice" the bases are in your campaign. It also depends on what your version of the Project envisioned the environment being like at "wake up" ... if it's an irradiated hellscape, the base crew will want to stay inside more, and the bunker will have more amenities. If they expected everything to have "blown over", there won't be as much reason to hunker in the bunker after waking up.
I understand that 4th Edition has "Project dependents", chosen ... somehow. Wives, parents, siblings, in-laws, children, cousins ... ? Anyway, those folks won't be so happy to be locked up underground. Or or they in special "kin and kinder" bunkers?
SPOILER FOR OPERATION: DAIDALOS
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The Morrow base presented in the new scenario book has a swimming pool and other nice things, presumably all to be used post-wake-up.
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Michael B.