Hi wes. Your friend is right. Lots to see. I'd suggest a couple of things. 1st, go to Old Spitalfields Market , wander the market, check out the The Ten Bells (Apparently one of jack the rippers pubs) and eat in one of the many nice restaurants there, see Brick Ln, go to a club, like 93 Feet East , or bowling at All Star Lanes . It's all being redeveloped so it's very different from what it used to be.
Also, get the tube to Wapping London Overground Station , go right out of the station and walk along the river. You'll pass old wharfs, lovely old pubs, Shadwell Basin , and you'll get a sense of what the working Thames used to be like. Eventually you'll get to Canary Wharf (60-90 mins), where you can do some shopping, visit the Museum of London Docklands (free and interesting, all about the sea trade, growth of the area, and slavery, worth your time). Theres a tapas place right on the river called Camino , great in summer.
The closest to the real east end is probably now Hackney though others might dispute this. Even the square east Enders was based on has £700k flats in it, times they are a changing'. You could go to mile end, walk along the canal and through Victoria Park to Hackney.
Honestly, don't be scared, it's great over here...
edit: Have you been to Maritime Greenwich ? the problem with the east end is lots of it got bombed in the 2nd WW, and traditionally it wasn't the place for architecture, but Greenwich has the naval colleges (lovely buildings) and the Meantime Brewing Company in the grounds, the National Maritime Museum , the Cutty Sark - The Sailing Ship and lots of old pubs and new restaurants. If you are a walker and get to canary wharf, there is a foot tunnel under the thames from Mudchute Park (south of Canary Wharf ) to Greenwich.
The East End isn't so gritty and dangerous if you avoid the more out-of-town parts - it's actually one of the most gentrified places these days. Shoreditch especially - hipster paradise!
Brick Ln is a must-see, especially on a Sunday when there's Brick Lane Market . Hop on the overground to Shoreditch High St or get the tube to Liverpool Street and walk from there. Grab an authentic Jewish-style bagel at the 24-hour Beigel Bake - a bargain, try the hot salt beef! There are plenty of nice pubs and bars around there as well, and lots of little independent shops selling quirky things. It's a nice place to explore!
If you're into vintage/second-hand clothing, there's a lot of vintage shops around Cheshire Street just off Brick Ln - further down there's the massive Beyond Retro , a huge warehouse full of vintage clothes. Can be a bit pricey though, and if you're from the states you've probably got a better range over there!
Also, what do you like? Walking, drinking, clubbing, history...? Let us know and we can advise more...