This is a short curated list of sites around the city that you may want to visit on your own.
Address: 55 Lime Street, Ouseburn Valley, Newcastle upon Tyne NE1 2PQ, United Kingdom
Prices: $9.82 for two hours
$7.64 for one hour
Hours: Monday, Wednesday, Friday 1:30pm
Thursday 6:30pm
Saturday 10am and 1pm
Sunday 1pm
Address: Castle Garth, Newcastle upon Tyne NE1 1RQ, United Kingdom
Prices: $9.23
Hours: Everyday 10am-5pm
*Last entry 4:15*
Address: S Shore Rd, Gateshead NE8 3BA, United Kingdom
Prices: Free Entry
Hours: Everyday 10am-6pm
*Last entry 5:45*
Address: Blandford Square, Newcastle upon Tyne NE1 4JA, United Kingdom
Prices: Free Entry
Hours: Weekdays 10am-4pm
Weekends 11am-4pm
Address: Barras Bridge, Newcastle upon Tyne NE2 4PT, United Kingdom
Prices: Free Entry
Hours: Monday- Friday 10am-5pm
Saturday 10am-4pm
Sunday 11am-4pm
Address: 16 Stoddart St, Shieldfield, Newcastle upon Tyne NE2 1AN, United Kingdom
Prices: Free Entry
Hours: Everyday 10am-5pm
Address: Castle Terrace, Warkworth, Morpeth NE65 0UJ, United Kingdom
Prices: $7.87
Hours: Wednesday- Sunday 10am-4pm
To get to Warkworth Castle also go to Newcastle Central Station and take the Metro to the Regent Centre Metro Station, walk two minutes to Regent Centre Metro Std B and take bus X20 to Alnwick. Then get off at Warkworth Market place Northbound and walk 4 minutes to Warkworth Castle. Or you can take the Metro from Newcastle Central Station to Newcastle Haymarket Metro Station. From there walk 4 minutes to the Haymarket bus station and take either bus X18 to Berwick upon Tweed or Bus X20 to Alnwick for either bus you will get off at Warkworth Market Place northbound and walk 4 minutes to the Warkworth Castle. The link above gives further instructions on which bus/train to use and the times they run.
Address: Durham DH1 3EH, United Kingdom
Prices: Free Entry
Hours: Monday- Saturday 7:30am-6pm
Sunday 7:45am-5:30pm
To get to the Durham Cathedral by train it shouldn’t take more than 30 mins. Start by going to Newcastle Central Station. From there catch the rail train to Durham and it’s a short walk, about 15 minutes, from the Durham station to the Cathedral.
The Cathedral Church of St. Nicholas
Address: St. Nicholas Sq, Newcastle upon Tyne NE1 1PF, United Kingdom
Prices: Free Entry
Hours: Monday- Friday 7:45am-6:30pm
Sunday 7am-5:30pm
Saturday and holidays 8am-4pm
Address: Clayton St W, Newcastle upon Tyne NE1 5HH, United Kingdom
Prices: Free Entry
Hours: Monday- Thursday and Saturday 8am- Dusk
Friday 8am-2:30pm
Sunday 8am-7:30pm
Address: Grainger St, Newcastle upon Tyne NE1 5QQ, United Kingdom
Prices: Free Entry
Hours: Monday- Saturday 9am-5:30pm
On Sundays it’s closed
Address: Grainger St, Newcastle upon Tyne NE1 5JG, United Kingdom
Prices: Free Entry
Hours: Monday and Tuesday 9am-4pm
Wednesday- Saturday 9am-1pm
Address: Barrack Rd, Newcastle upon Tyne NE1 4ST, United Kingdom
Prices: $16.28
Hours: weekdays 12:30 and 2:30
Weekends 11:30, 12:30, and 2:30
Address: Turret Road, Newcastle-upon-Tyne, Tyne and Wear, NE15 7TH
Prices: Free Entry
Hours: Any reasonable daylight hour
Address: Life Science Centre Times Square, Newcastle upon Tyne NE1 4EP, United Kingdom
Prices: $13.02
Hours: Monday- Saturday 10am-5pm
Sunday 11am-5pm
Address: Pier Rd, Tynemouth, North Shields NE30 4BZ, United Kingdom
Prices: $6.84
Hours: Saturday and Sunday 10am-4pm
Address: 100 Grey St, Newcastle upon Tyne NE1 6BR, United Kingdom
Prices: May vary on the show you choose
Hours: May vary on the show you choose
Travel Info: Newcastle to Durham Cathedral and Warkworth Castle
http://jplanner.travelinenortheast.info/nexus
To get to any of these locations you can use this link or google maps. Most of the websites also tell you how to get to that attraction.