Is there a specific word that describes people who are easily impressed?
Consider susceptible ("likely to be affected by something", "easily influenced or tricked; credulous" and "(medicine) especially sensitive, especially to a stimulus"); and also consider impressionable ("Susceptible of impression; capable of receiving impressions; emotional"). An "impressionable person" may be someone on whom it's easy to make an impression, or may be someone at a formative stage such that impressions will last. Note, making an impression on someone can differ from impressing them.
Gullible, naive, guileless, ingenuous and unsuspecting might get close, but I doubt if there's any single word that specifically captures the 'easily impressed' sense.
Credulous is not quite right (too easily believe things rather than are impressed by them) but may work depending on what the situation is you are trying to describe.
Rube often carries this connotation, but it also has more of a condescending tone.
From Merriam Webster: 1: an awkward unsophisticated person : rustic 2: a naive or inexperienced person