I'm hitting Munich today!
I'd translate this as
Heute geht's (weiter) nach München!
I'd insert the weiter if you want to express that you are at one place now and are continuing your travels. For example:
Letzter Tag in Nürnberg - heute geht's weiter nach München!
In that sense you could also say:
Heute ist der letzte Tag in Nürnberg. Weiter geht's nach München!
You could also say
Heute geht's nach München if you live in another nearby town and want to say that you're going shopping in Munich or something.
In the sense of Merriam-Webster, which I understand as
we're going to the place in town where people go to go shopping or to go out, a possible translation would be:
Heute gehe ich in die Stadt.
Heute geht's in die Stadt.
where die Stadt does not refer to a specific city. In that case die Stadt refers to the area in a city where things happen - cafés, shops, shipping centers, etc.
In Germany, this tends to be the center of the city (in former times, this was the central market place. The cities grew from there). Ironically, this is also sometimes called die City in German. When you talk about Munich you will often hear people say Heit gemmer in die City (Heute gehen wir in die City).
Due to the fact that the so called Stadt used to refer to some more or less central area of a city, you could also say
Heute fahren wir nach ... rein.
assuming that you stay anyway outside that inner city.
For example if your hotel is in the outskirts of Munich, you could say:
Heute fahren wir nach München rein.