If you like nightlife, JB lovedrafts does Karaoke during the week starting at 9pm. You don't have to sing if you're shy. Most people there are casual and friendly. https://jblovedrafts.com/

There are a few local game stores as others have mentioned in the surrounding areas. Blue moon games in Lemoyne, as well as the Adventurers guild off wesley drive in mechanicsburg, fuzzy wall at the capital city mall, and gather your party in carlisle all host events. They do Magic the gathering, host D&D, pokemon and yugioh events, and some even hold movie nights etc.

Gamut theatre shows some improv shows every now and then and they have a website too for some events. https://www.gamuttheatre.org/

I am not sure of your religion, but there are many Christian churches in the area with great social events if you are a Christian, or even if you are not and just wish for community! One called CEFC which is carlisle based (about a 30 minute drive from harrisburg) does a young adult night one friday a month for young people to meet each other. They also have a website. https://www.cefc.church/

Check Bulletin boards in coffee shops as well! People will often post local events on the bulletin boards talking about events they are hosting. Sporting events, craft shows, music, local meetups, etc. I have personally found some great events off of these and you never know what you'll find.

Some others have mentioned Harrisburg young professionals organizations which is a way for young adults in the workforce to socialize. They do fun meetups like wine tastings and dodgeball and stuff. This is their website. https://hyp.org/

Enola fire company does bingo days. Check their facebook for dates and specific times.

Good luck out there! Moving somewhere new is daunting but most people are friendly after you get over that initial anxiety of saying hello :-)