Long story short:
Let's not go is simply 行くのは止めましょう
If we use 行かないことにしましょう it is more like Let's decide to not go
I think 行くのは止めましょう is a stronger Let's not go compared to 行かないことにしましょう, though I'm not sure (someone may wish to verify / de-verify it)
As the -おう/こう/.../よう and -ましょう forms have no negative, the まい ending is sometimes used in the situation of expressing negative intention. It cannot be used to express a "let's not" situation, and in any case is a literary form and rarely seen at the ends of sentences, however it is fairly common in a dependent clause to show one's strong determination not to do something, as in
私は、彼女とは二度と会うまいと思う。 (I'm certainly not going to see her ever again!)
Often "Let's not do ..." is expressed by saying "Let's stop doing .." using 止める or 止す. E.g.
パーティーに行くのは止めましょう。 (Let's not go to the party.)
Another construction which means "let's decide to" or "let's try to" is verb+ことにしよう/しましょう or verb+ようにしよう/しましょう. For example:
名古屋までバスで行くことにしましょう。 (Let's [decide to] go as far as Nagoya by bus.)
This construction can be used where appropriate in negative sentences.
バスでは行かないことにしましょう。 (Let's [decide to] not go by bus.)
Note that that are many verbs where the volitional/hortative forms cannot be used in a meaningful way. One cannot say "午後に雨が降りましょう", for example. On the other hand, one might hear rockers on the stage yelling:
のってるか？今夜は燃えようぜ！ (You guys getting in the mood? Let's burn it up tonight!)
The まい auxiliary can also be used to carry the sense of "probably not". As with the use of まい in the volitional category, this usage is strictly literary.
彼はもう英語を教えるまい。 (Most probably, he won't teach English any more.)
The -ないだろう form has the literary alternative form: なかろう.
http://www.csse.monash.edu.au/~jwb/wwwverbinf.html (there's alot of goodies packed in that small page ;)