If you're vegetarian (or even not), Inn Season Cafe is a great place in Royal Oak...it's small, but nice atmosphere.
If you like Thai food, Rexy's Bangkok Cuisine in Royal Oak is a great combination of good food and atmosphere. It's family-friendly too.
If you like sushi, go to Izakaya Sanpei in Plymouth (very close to Livonia by the way). It's the best Japanese food I've ever had in the Midwest and usually, I'm the only Caucasian eating there when I go, so I take it as a good sign

Plymouth is a very cute downtown you can walk around in btw.
If you want a brewery type of place, try Rochester Mills Brewery. Also, Kruse and Muer is a great restaurant in downtown Rochester. Rochester is a cute little downtown about 45 minutes north of Livonia.
A large chain of Lebanese restaurants that is still great for being a chain is LaShish...They have one in Livonia. Great pitas and a killer garlic spread there.
If you want Greek food, Greektown is the place to go...It's in dowtown area of Detroit. All the restaurants are great there! Also, there's Mexicantown too and you can't go wrong at any of those restaurants either.
Sweet Lorraine's is a cute, quaint place too. They have one in Southfield now I noticed which is not far from Livonia (maybe 15 minute drive).
If you want to venture to Ann Arbor, which is 20-30 minutes from Livonia, you won't find a shortage of restaurants. I highly recommend a Korean place on the outskirts of Ann Arbor called Seoul Garden...It's the best

Ann Arbor is a great college town you'd absolutely love.
If you want to have Ethiopian, the Blue Nile has locations in Ann Arbor and Ferndale. Just be ready to eat with your hands...I love the veggie platter.
Great Indian places...Rangoli in Auburn Hills/Rochester border; Priya in Troy; Ashoka in Troy and Canton (btw, Canton is near Livonia too and Plymouth). Both Indian places are not chain restaurants in Troy

Speaking of non-chain restaurants in Troy...Mon Jin Lau is a great Chinese and Asian fusion place to eat...It has a great ambiance.
There's lots of BD's Mongolian BBQ's if you like that sort of thing...Let's see in Novi, Dearborn, Ann Arbor, and Royal Oak.
If you like Italian, I highly recommend Roma Cafe in Detroit. It's old school and old world...hell yeah!
Let me know if you need more help...I've eaten everywhere LOL
