Getting to and from the ground
The options are:
- train from Liverpool Central or Moorfields to Kirkdale (eight an hour, journey time 8-9 minutes from Liverpool Central, or 6-7 minutes from Moorfields), then around a 15 minute walk to the ground; you're covered for this if you've got a ticket to "Liverpool stations"
- train from Liverpool Central or Moorfields to Sandhills, then 'SoccerBus' to the ground (2.30 single or 3.80 return, or 1.90/3.30 if bought as an add-on to your train ticket)
- taxi (good value if there are five of you to fill a black cab)
- bus from Queen Square bus station (17), or SoccerBus (919) from Commutation Row  (2.30 single or 4.40 return)
After the game you could either go back to Kirkdale, or there are buses back to the city centre from Walton Lane. Be careful that you get on the right one though as the first ones you come to will be going to Sandhills. You should be able to make the 22.08 train if you leave bang on the final whistle and get a move on to the bus.

If you're driving over, try to get there reasonably early and park up near Anfield and you'll be well placed for getting away after the game.
As far as pubs are concerned, it's horses for courses. There's a load around the ground and in particular along Walton Road and County Road, and the only one I'm aware of as being totally no-go for away fans is the Royal Oak. It goes without saying that the nearer you are to the ground the busier they're likely to be. There's a Wetherspoons (the Thomas Frost) on Walton Road, which welcomes away fans and is the only place anywhere near the ground where you can get cask ale. It does though apparently get chocka. If you're driving over and park somewhere near Anfield you might want to drink in the one of the pubs around there. The Arkles is an old favourite. It has cask ale on for Liverpool home games, perhaps it's the same for Everton games.

If you get the train over then you may prefer to drink in the centre until late on, in which case you're spoilt for choice. We have been known to go to the Richard John Blackler just down from the station. However, it's notorious for bad service, so I would give it a miss. You'd be better off going to the Crown, which you pass on the way to the Richard John Blackler. It's a traditional pub which has a decent selection of beers and pub food at reasonable prices. More or less next door is the recently opened Lime Street Central, a Greene King pub. Also recommended are the Ship and Mitre, which has a vast selection of beers from both the UK and abroad, and the nearby Excelsior, which is very much like the Crown. From both of these it's a five minute walk to Moorfields station. Another option is the the Globe. This is a traditional cosy little pub, with great staff and friendly customers, not to mention a good range of beer. Plus it's literally two minutes from Liverpool Central station. Other places you might want to try are Doctor Duncan's and the Poste House, both of which have a good range of beers and get decent reviews. There's another Spoons right next door to the station, the North Western. It's got a similar feel to the Union Rooms.

All the pubs mentioned, plus a few others, are shown on the pub maps below.

Goodison pub map
City centre pub map
Liverpool pub guide (very comprehensive and fairly up to date)
Football Ground Guide
Official Everton site
Official matchday guide (2018/19)
Soccerbus info