Gettysburg is a somewhat uniquely rewarding battlefield to visit because of it's relatively open terrain and it's elevations that give wide vistas, making the fighting easier to envision and understand. Unlike say Chickamauga, which though well preserved, is basically a big woods interspersed with small farm lots and is a very hard battle to understand. And Gettysburg was also a series of dramatic crisises for the Army of the Potomac, one after another, crisises that were usually met when Hancock, Warren, Humphreys, Vincent, Gibbon, Stannard and many other officers, often on the brigade and regimental level, stepped up at the spur of the moment. The Army of the Potomac was finally functioning pretty well.
Anyway, I suggest you read Coddington's classic book on the campaign and battle before you go. Print yourself a copy of the still very useful <old> guidebook from the NPS website, link below.
Visit Culps Hill, many miss that and the fighting there was as vital as any. And visit where the Federal 1st Corps fought west of town on the first day, including the railroad cut west of town where Wisconsin men of the "Iron Brigade" made an audacious across the grain attack and corralled and captured a rebel regiment.
On the 11th Corps line north of town see the monument of the 82nd Illinois, the only Illinois infantry regiment in the Army of the Potomac. (No doubt they would've been happier with Grant's heavily Illinois Army of the Tennessee which was winning the victory at Vicksburg at the same time Gettysburg was fought.) Then wonder why Howard, who'd poorly commanded the 11th Corps during it's whippings at Chancellorsville and Gettysburg, was later given command of the Army of the Tennessee by Sherman during the Atlanta campaign. Old Uncle Billy is hard to figure.
Along Cemetary Ridge, on the 2nd Corps line of the second day, see the statue of Father Corby placed where he gave the Irish Brigade mass absolution before they entered the fight. And see the brigade's impressive monument, a large bronze Celtic cross, on the Stoney Hill near the Wheatfield.
https://www.nps.gov/parkhistory/onli...hh/9/index.htm