Asilomar is just a few miles from Monterey. Pacific Grove, the town in which Asilomar is located, is very small -- tiny, in fact; and the two towns are adjacent to each other. Have a look at a Google map!

Driving distance from Asilomar to the Monterey Bay Aquarium (just as one example): only 2 to 2.5 miles, depending on route! And, distance from Asilomar to Passionfish (venue for Saturday night dinner): just over a mile!

By the way, I heartily endorse staying at Asilomar. It's not for those who need their luxury, however -- it is rustic and/or somewhat spartan, depending on which type of lodging you choose (it was built in more or less four phases, starting in 1913, so the early, Julia Morgan, phase is rustic and the later phases more modern). The TravelZoo special mentioned by jumpdogjump above($119 + tax) actually appears to still be available, but requires a one-night deposit. Sometimes there are better deals available. Also, a lot (maybe most/all?) of the historic (rustic, wood-paneled, designed by J. Morgan) rooms have just one single-sized bed, so, that room type may not work for a couple.