Welcome! There's a farmers market every Saturday in Horner Park at Montrose and California. Some of my favorite restaurants in the area include Ixcateco, Semiramis, LD Pho, and smalls (last one is technically in Irving Park).
We love the farmers market in Horner Park as well. We love Great Sea restaurant which is Chinese by Lawrence and Kedzie. We love love Maries pizza which is technically Mayfair also Rojo Gusano is MUST they have yummy margaritas! So is T & B grill they have a great brunch menu and they're burgers are delicious. Ixcateco is also very good! Good luck and welcome
Horner Park Farmer's market is pretty small. If you can make it to Logan Square I highly recommend it! I also find Albany Park lacking with restaurant options - Lincoln Square and Andersonville have better variety!
Dining out - in addition to what's already been mentioned (esp Rojo), Hella's Greek Bakery on Lawrence has great spinach-cheese pies for carry out. I've heard good things about Bryn Mawr Breakfast Club in North Park. Baker Miller. Festivals - there are a couple specific to AP, the AP Festival and in spring, and there is a dining one along Kedzie Farmers Markets - Horner Park, Lincoln Square and Andersonville's are the three closest; I'm not sure if the refugee farm next to Global Garden is still going. Volunteer Opportunities - check out Chicago Cares.
Logan Square is far from Albany Park - farmer's market is at Independence Park on Irving Park Rd just east of Pulaski. Also Six Corners...depends on where you live as to what's convenient. Get the list of markets off three city website.
We have absolutely loved living in Albany Park. We are just south of Foster so we frequent more of the north side of Albany Park. I can not say enough about the Bryn Maur Breakfast Club. Excellent breakfast and lunches. Merla's on Kimball, just north of Foster has wonderful Filipino food and you will always see Merla cooking. She is super cute and beyond nice. The Lawrence Street Fish Market has some of the best sushi in the city. Do not be afraid of the looks of it, it is raved about by all who have gone but it is CASH ONLY. And if you are looking for wonderful thin crust pizza, you can't beat Maries on Lawrence. The tacky décor just adds to the flavor of the food.
Enjoy your new neighborhood. We are moving to another neighborhood as we have purchased a house, but we will always come back to Albany Park as we have loved our 8 years here.
I really love the Horner Park farmers market - it's small enough you see and chat with your neighbors, but has enough stuff to always find something interesting - get a coffee from bru and tamale for breakfast. Plus, free yoga at 10!
Everyone has covered the awesome neighborhood restaurants - Nighthawk is a pretty great addition for both coffee in the morning and drinks at night.
Consider volunteering at the Friendship Center on Lawrence.
Welcome and congratulations on your new home. To add to the list of local restaurants - THE ALPS on the corner of Elston and Irving has fabulous breakfasts - it is often busy on Sat/Sun morning but it is a big place and they move fast. We go almost every weekend and feel like family there. Also, for traditional delish Italian, Sabatinos on Irving Park just west of the highway. They have a nice patio and the food is always excellent and very generous portions. Honey Butter Fried Chicken at Elston and Roscoe is also a local fave, Logan Square has the biggest farmers market around but there is a nice market every other week at Independence Park (I forget if it is Sat or Sun but I am sure the schedule is online) and every Sat there is a small but nice market in Horner Park. The Hornere Park market is only a few years old and seems to expand every year - I havent been over there yet this season but hopefully this weekend! Lincoln Square (tues am and thurs pm) and Andersonville (wed pm) have mid-week markets, if you dont mind travelling a bit out of the area.
Rojo Gusano's has delicious tacos and mezcal. My daughter and I also really love the brunch there. She gets the chicken and waffles and I get the ChilaKillers and Rompope. Ruk Thai is great for Thai cuisine. We do Hot Dog Station for American fast food fare (gyros, italian beef, French fries) Nighthawk for coffee, spiked and unspiked. Kabobi and Noon-A-Kabob are hot contenders for Persian. If you don't mind wandering into Mayfair territory there is a Peruvian restaurant, Ay-Ay Picante and a Cuban Restaurant, (forgot the name) both on Elston. The big festival in Albany Park is World Fest.