If you are working near Lancaster, no way I would live in Addison. That would be like an hour commute on a decent day. If you want a house, don't be afraid of the southern burbs like Lancaster, DeSoto, Cedar Hill, or even Grand Prairie. Even Mesquite and Garland. Those places mentioned are called the "black burbs" by some. You'll never see people recommend them on a site like City-Data because they think anything south of Plano is poor and ghetto even though the wealthiest parts of the city are south of Plano.
Based on what you said I would recommend:
Uptown - closest we have to something East Coast. 1200 would be decent for rent. Lots of nightlife you can walk to. Has a subway stop and a streetcar that runs through. Womenz of all races everywhere. Katy Trail(elevated running trail) runs right through there. American Airlines Center is right next to it. Downtown is right next to it. Best Hotels are next to it in Turtle Creek(ritzy high rise and mansion area), Highland Park is next to it. Knox-Henderson is next to it(another nightlife area). Less for your money though. Always new projects going up to keep the prices at bay.
- downtown(some decent places that would surprise most that even live in Dallas), You could get more for your money downtown. Not as nice as Uptown, but lots of new renovations. Close to Uptown and lots of clubs and venues on Main and Elm as well as the West End. Really slept on by most in our area.
Knox/Henderson - This area is just north of Uptown, so its a little more chill. Lots of nightlife though. Way underrated by those that don't know Dallas. This is the area around Knox Street which is west of Central Expressway and Henderson St(same street but changes name east of Central Expressway) Cheaper than Uptown and a little more neighborhoody. Lots of townhomes and apartments. Lots of restaurants and little clubs. And Henderson runs right into Lower Greenville which is a similar place.
- Old East Dallas/Lakewood - Another area that's often overlooked. This is where I live. Nice mix of hood, middle class and wealthy all in the same area. Pretty chill area. Lots of young people in the older, renovated apartment complexes to the east and newer complexes to the west. The Lakewood neighborhood is in the center of this and is where lower Greenville and Knox-Henderson meet, so lots of nightlife, diversity and is more quiet than the others. Easy to get to the other parts of town to.
- North Oak Cliff - . Its always been kinda hood with a wealthy area sitting in the middle. Now the parts close to the wealthy area are gentrifying and apartments are starting to go up. Some decent neighborhood type nightlife. Similar to Knox-Henderson but across the river from downtown and smaller. Look near Methodist Hospital or Bishop Arts where most of the development
- The Village - If you are younger and don't mind something a little more suburban, The Village is a big area of apartment complexes north and west of SMU. Very few black people there, but its a great location and you could live like a king. Close to NorthPark(biggest, most popular mall here), Upper Greenville(suburban nightlife area), and 10 minutes from those other areas mentioned. Only downside is students like to live there too. But probably the best daily sightseeing unless you live in the West Village area of Uptown.
- Farmers Market/Deep Ellum - This area is often forgotten, but is right next to downtown. Deep Ellum is not great these days, but its not bad. Most people live in the northern part of this area or to the south in the Farmers Market. Lots of apartments. Lots of young people. Close to everything.
Long yes, but probably worth a read since you don't know the area. Just avoid the Nawf(northeast Dallas mainly around Skillman and Audelia Rds) South Oak Cliff (Dallas nearest the DeSoto/Lancaster/Cedar Hill)and South Dallas which is the area just south of downtown and east Dallas).