If you arrive by train it's only a 10 minute walk from the station to the ground.
If driving down then the best area for street parking is around the Mustard Pot pub (see pub map). Any nearer to the ground and it's permit holders only. There's a big match day car park to the south of the ground at Norfolk County Hall. This will set you back a few quid, and you could well find that it's full if you arrive after about 2 o'clock.
The pub I was in last time I was at Carrow Road, only a couple of hundred yards from the away turnstiles, has since been demolished. Nowadays the most popular pub with away fans is apparently the Compleat Angler, just over the river from the station. Back in 1985 I was in there when we played Norwich on the last day of the season, the day of the Bradford Fire. At that time the pub was run by former Toon player Albert 'Ankles' Bennett. I suspect he's not there now. In any case, the pub hasn't really got anything going for it, and they'll almost certainly be using plastic glasses, so I suggest you give the place a wide berth. In any case, there are much, much better options. Less than 10 minutes walk from the station is the Jubilee, a lovely traditional pub far enough from the ground not to get too busy on match days. They've got a good range of beer, a beer garden, and two pool tables. What more could you want! A bit closer to the ground is the Coach and Horses, which is actually a micro brewery as well as a pub. Like the Jubilee. it gets universally good reviews. The only possible reason for wanting to give it a miss is that it gets very busy on match days!
West of (and uphill from!) the ground there's a cluster of decent pubs. Best of the bunch could be the Kings Arms, a Batemans pub offering thirteen real ales "of all styles including pale, golden beers, through to mild, stouts and porters from many regional and microbreweries both local and farther afield", as it says on their web site. Worth trying I'd say.
All the pubs mentioned above, as well as quite a few others, are shown on the pub map below.
Internet Ground Guide