[susan53]

g) The man was staggering/lurching/tottering/wobbling outside the pub. (Is totter also used when you feel weak or dizzy?)

wobble : let's get rid of this one first - it's not relevant here. wobble means to be unbalanced and therefore to move unsteadily from side to side. It could be used, for example of someone learning to ride a bike or to ice-skate. this example comes from an text describing an exercise for body-builders called the "one-leg lunge" :Oh, you'll wobble and weave quite a bit at first. Notice that there's no forward movement involved, and the sideways movement is quite small - too small for this context, where rather than wobble I would choose sway to describe the sort of drunken movement from side to side which you probably mean. sway involves larger movement :
The trees swayed in the wind.
He slowly stood up, swaying like a drunkard.
Again, no forward movement is being described here.

stagger : this is fine in this context, and means to take a large uncertain steps, as if you were about to fall. However, in the examples I've found, it is predominantly used with a prepositional phrase or adverb specifying the direction of the stagger:
He staggered back to the group.
He staggered into the back seat and lay back
He staggered round the rear of the couch
Fists pummeled him as he staggered forward.
So your example wopuld be more natural as :
The man was staggering around outside the pub.

The same is true of lurch ( implying very large, sudden and erratic movements) and totter (small, unsteady steps). Some examples :
The car lurched along..
He lurched on down the road despairingly..
The little child tottered over to its mother...
so again, I'd add around to your example if I used these verbs.