As stut has said, the train journey *should* be under 3 hours each way on a normal day, so 4 hours would suggest that you're getting hit by weekend/ easter engineering works (or you've specified some departure point other than King's Cross).
If prices are equal, I have tended in the past to fly southbound and get the train northbound. This is because Newcastle Airport is small and manageable compared to the hell of LHR/ STN (and the unreliability of transport in the capital). T5 promises to make the northbound trip a bit more reliable...
The queues for check-in (if you need to do that) and security at LHR/ NCL will be the same whether you are travelling domestically or internationally. They're promising no queues at T5. At either airport, 2 hours is overkill unless you like airports. At NCL, there's no sweat arriving at T-30 mins if you've OLCI'd and have no baggage. You'll most probably be airside within 5 minutes of arriving on the Metro, and the BA gate is one of the closest to the departure lounge - 3 mins walk max. At LHR T5, there is to be a 35 minute cut-off time by which you must have passed through security. I'll let someone more expert than me tell you how long it will take from your T4 hotel to T5.
Newcastle's a great city. The centre is about 25 min from the Airport by metro. Get off at either Haymarket or Monument (can recommend a few places for brunch if you like) and you can either wander through the compact city centre and down Grey Street (the most elegant street in the UK, apparently) or switch to a bus to take you down to the Quayside area (Tyne Bridge, Baltic Arts Centre (great views from the top floor), the Castle Keep, Millennium Bridge, there's also bike hire if that's your thing).
Carry on walking (downstream) and you get to the Ouseburn Valley and Jesmond Dene - a small river flowing into the Tyne along which various funky pubs ply their trade. You can walk up the Ouseburn into the suburb of Jesmond and eventually end up back in the city centre.
If it's a nice day, you can catch the Metro out to the beach at Tynemouth. There's a market in the Victorian station on the weekend.
If you're walking back into Haymarket/ Monument station at 1730, you'll have plenty of time for a 1900 flight.
Hope this helps - feel free to ask any more questions.