West Brom

It's impossible to get back to West Yorkshire by train unless you're prepared to leave the game at half-time. You can get back to Sheffield, but not until 10 past 1.

Getting to the ground
You can catch a tram from outside New Street (Grand Central stop) to Hawthorns, which is only a 5 minute walk from the ground. The tram runs every 6 minutes at peak times, every 8 minutes on Saturdays, and every 15 minutes evenings and Sundays, with a journey time of 15 minutes from Grand Central. It costs around 4.50 return. Alternatively, you can walk to either Moor Street or Snow Hill station and catch a train to Hawthorns. They normally run every 10 minutes, but only every half an hour on Sundays. The journey time from Moor Street is 11 minutes. The good thing about the train is that it can be free. because a ticket to Hawthorns is usually the same price as to New Street. And even if you do have to pay, it's around 2 quid (even more with a railcard!) less than the tram.
If you're driving down then there are a few private matchday car parks at some industrial units near the ground. There is also free street parking though. You could probably do worse than to park by the Vine if you arrive reasonably early. It'll be a bit of a hike back after the game, but you'll be back on the M% in no time. Again, Albiontillwedie has very comprehensive parking info on the Matchday Guide page.
It's a virtual desert around the ground when it comes to pubs, so if you arrive by train your best bet is to have a few pints in the city centre and then catch a train or tram at the last minute. The best pub in the centre is arguably the Wellington, roughly half-way from New Street to Snow Street. This place is an absolute gem, having no less than 15 hand-pulled beers on at any one time, as well as a good selection of foreign beers. The only slight drawback with the pub is that it doesn't do food; however, they provide plates and cutlery for anyone who wants to consume their own food on the premises. To get to the Wellington from New Street, follow the signs for the Stephenson Street exit, and then follow the route shown on the city centre pub map below. The Old Contemptibles is another pub worth considering as it's right outside Snow Hill station, although it does only have a mere nine hand pulled beers on! For fans of Wetherspoons there's the Briar Rose, just down from the Wellington. An alternative to drinking in the centre is to jump on a tram to Benson Road or Kenrick Park (see next paragraph for more info on pubs).
For anyone driving then the most popular pub for away fans, and also the nearest to the ground, is the Royal Oak, right on the A41. It will no doubt get very busy, so you may want to keep on going on heading down the A41 where you will (eventually!) come across some other pubs. For a lot of fans though the only pub worth thinking about is the now legendary Vine. It's basically the food that has made this place an institution. Not to be missed on a match day is the indoor barbecue at the rear of the building serving freshly grilled chicken tikka, shish kebabs, tandoori chicken, and naans. As for beer, they have a number of craft ales, as well as cask beers from micro breweries. The Vine's a bit tricky to find, but the Hawthorns pub map below has the shortest walking route from the ground marked. Or catch a tram to Kenrick Park! The main drawback with the Vine is that it will get ridiculously busy. On top of that you'll probably have to put up with plastic glasses. The lack of pubs directly around the ground might tempt you to jump on a tram to somewhere farther afield. West Bromwich town centre would be an obvious place to aim for. However, the pubs there are "very partisan", attracting a heavy police presence. Better is to head in the opposite direction, getting off at Benson Road. From here it's less than a five minute walk to the Black Eagle. A winner of the local CAMRA branch's pub of the year award on numerous occasions, the Black Eagle gets universally good write-ups. Nearby is the New Soho Tavern, which apparently does amazing Indian food.

Hawthorns pub map
City centre pub map
Football Ground Guide
Tram info
Birmingham CAMRA
baggies.com (good unofficial site)
Albiontillwedie (another good unofficial site)