First of all, you are giving mixed messages within your question.
You want to loose the remaining fat around your belly, and understand that it takes a long time to lose that last bit, but you also said you already met your goal, and want to be able to reward yourself with junk food and beer. In addition, you have already set yourself up for failure by stating that your diet will never be perfect.
Here's the thing...
That last bit is the absolute hardest to lose. You need to really commit to taking it off, or be okay with not losing it. Pretending like maybe it'll just slough off if you sort of eat okay still, is thoroughly unrealistic.
What happens to lots of people, is that they reach an intermediate goal, reward themselves, and start to slide backward. It takes a lot more work to lose weight than it does to maintain a weight. If you can ramp up the intensity in the homestretch, you can get the rest of the weight off...if that is what you want to do.
The best beginner weight training routine is a circuit made up of 3 movements done consecutively...a push, a pull, and a squat. You do each exercise one after the other resting minimally between sets of 20, and repeating for 2-5 circuits.
A push movement can be a bench press, any cable exercise simulating the same pressing motion, or even an overhead shoulder pressing movement.
A pull movement would be a low row, bent row, one arm row, or you could substitute a lat pull.
A squat movement could be a free bar squat, dumbbell squat, leg press, or lunges.
I didn't mean to be so hard on you, just trying to keep you based in reality.
Considering that you have not incorporated weight training into your routine thus far, I imagine that when you do, you'll push past your current plateau. I can not say whether it would be a couple months or a year to get your weight down because everybody is different. Plus, I'm not sure what your weight was/is because it doesn't read clearly in your original post. That information could help me to lend more insight in that area.
Let me suggest that you start the circuit routine I described, and if you have not been incorporating a cheat meal already in your diet, that you start doing that also.
A cheat meal can stimulate your metabolism whereas strict dieting for an extended period can stall your metabolism. You have to be careful with a cheat meal and make sure you don't get out of control and that it doesn't become a cheat day (speaking from experience). Also, since it stimulates your metabolism, you may end up feeling more hungry which can require you to have even more resolve on your diet.
Leave the alcohol out of the equation for now.
I'd love to hear how you progress when you make these changes.