You're spoilt for choice, there's Llandegfedd Reservoir just up the road from Newport and the Afon Ebbw runs into the west of Newport offering some of the best brown trout fishing in South Wales.
There's day ticket water on the Usk between Caerleon and Abergavenny going north of Newport which is top class and easy on the eye.
If I were staying in Newport I'd go for one of the hotels in the Usk valley not too far from town. The Newbridge Inn might be a good bet -
The Newbridge Inn, Tredunnock nr Usk | LateRooms.com
Newport itself isn't pretty although it's improving but I remember in the 1970s there was a big fuss because a Japanese film company had chosen it a a location for a post holocaust film!
If you're on the Usk you probably won't want to budge but there's the Afon Llwyd for throw - away price fishing next valley west.
The Rhymney is the next river going west from Newport with Ynys Y Fro reservoir along the way.
Next stop, about 15 miles the Taff, my home river, minty fishing for big brown trout after 8 (pm).
Day ticket prices are extremely reasonable for river and reservoir, and easily accessible give us a shout nearer the time for the info.