By car
The most direct route to the Inner Harbor area from outside the city would be from I-95. Take exit 53, which dumps you on to Howard St. Parking can be messy and/or expensive, and garages will be the only option available. If you want to park on-street, you could try Fells Point to the east, which will leave you with about a 15-20 minute walk to the Aquarium.
By bus
Visitors to the city don't really use the bus system, but if you are feeling intrepid, there are a handful of useful routes.
#11 (http://mta.maryland.gov/s...), if you pick it up on Pratt St on the harbor, will take you east to the heart of Fells Point, and then on to Canton. If you take it from Lombard St one block north of the harbor, it will take you north up Charles St through the heart of Midtown and on to Johns Hopkins' main campus. The northern route returns to the Inner Harbor from Midtown via Cathedral Ave.#1 (http://mta.maryland.gov/s...) runs south on Light St through Federal Hill and on to Fort McHenry via Fort Ave.
By Water Taxi
Ed Kane's Water Taxi, (http://www.thewatertaxi.com) +1 410 563-3901, stops at the Rusty Scupper, the Science Center, Harbor Place, the Aquarium, Pier 5, and Harbor East, with connections to popular tourist stops in South Baltimore, like Fort McHenry, as wells piers in Fells Point and Canton to the east. Day passes, adults: $9.00, kids under 10: $4.00. May-December only.
By Circulator Bus
The Circulator has two relevant routes. The orange line (http://www.charmcitycircu...) will take you east on Pratt almost to the edge of Fells Point, with a quick stop in Little Italy, before returning west on Lombard and running to the University of Maryland, Baltimore. The purple line (http://www.charmcitycircu...) runs south on Light St to Federal Hill and north on Calvert St to reach Charles St through Mt Vernon and Midtown.
By Light Rail
Light rail (http://mta.maryland.gov/s...) lines stop at Camden Yards, running north through Downtown and Lexington Market, and on to Penn Station; south to BWI airport.