There is a dedicated multi-use path from Marina to Monterey although in both Seaside and Marina, parts of it put you onto streets for some sections. It takes you right to the Aquarium though. The only problem is that the Monterey section near the shoreline is often packed with tourists, strollers, dogs, rollerbladers, small kids and all sorts of hazards to cycling health. But it's a wide enough path that if you are paying attention and not trying to time-trial you can avoid trouble.