A couple of places come to mind:
- John Barleycorn (Lincoln Park) - I know it's packed with the young 20-something crown on the weekends, but it has a really nice outdoor space and is not that crowded post-work and during the day on the weekend.
- Uberstein (Wrigleyville) - Also packed on the Cubs game days, but they definitely have pretzels and an outdoor space.
Have you tried Sheffields? The food is really good, they have a beer garden and the beer list is great. I agree about Resi's if you're leaning towards sausages over beer, there is also Glunz down the street which has outdoor seating, as well as Laschet's, although I'm not sure if they have a garden or not.
Owing to the city's liquor laws, I can't think of too many 'beer gardens'. Plenty of bars have patio/outdoor seating but I can't think of many that would say 'beer garden' to me (Resi's, already suggested, notwithstanding).
Clark Street Ale House, River North, has a back patio that is completely surrounded by concrete high-rises. It's a nice enough space but the surrounding buildings detract from the experience. They don't serve food (but don't mind if you bring food in).
Some of my favorite bars with good beer and outdoor spaces include Twisted Spoke (great rooftop deck, decent food, amazing beer list), Cleo's on Chicago (large back patio, okay beer, eh food), SmallBar on Division (small-ish area out front for tables, great beer list, better than average food) and Big Star (limited but well chosen draft options, fantastic cocktails, no sausage other than their Sonoran-style hot dog (ie. hot dog wrapped in bacon in a bollito roll) and large, albeit always-crowded, patio seating out front).
501 N Ogden Ave, Chicago, IL 60642
Clark Street Ale House
742 N Clark St, Chicago, IL 60654
I'm not exactly sure what "a few miles from the loop" means, but the place you'd like to go is Resi's Bierstube. Lots of sausage and great beer with a very nice biergarten.
2034 W Irving Park Rd
(between Hoyne Ave & Seeley Ave)
Chicago, IL 60618
Resi's Bierstube Restaurant
2034 W Irving Park Rd, Chicago, IL 60618