Found this advice on MumAbroad Costa Blanca, will add more as I find them!
Restaurante La Vuelta
Recommended by Stella Robins
Situated near the beach, this restaurant not only offers fab food but also special themed evenings such as music and dancing and live entertainment. There is a kids menu, which is quite varied so should suit even the most fussy of eaters. 
Calle Vincente Blasco Ibañez 68 03140 Guardamar del Segura (+34) 966727559
 
Si Bar - La Manga Resort
Recommended by Linda Greet
Si Bar is situated in the La Manga club resort and appeals to all ages.  Not only is it a bar and restaurant it also has a fantastic out door play area for the children making it a very family orientated bar.  They have regular live entertainment which includes a children´s entertainer.  So you can relax knowing your child is in safe hands.
(+34) 968175000 www.si-bar.eu
 
Laurel and Hardys
Recommended by Keeley Carwich
As the name suggests this restaurant serves English food (which is really good quality). Staff are really friendly and there are pool tables and tvs for older kids as well as bouncy castles and climbing frames for the younger ones. You can either sit inside (in the aircon) or on the large terrace outside. In the summer months the terrace is open from 12:30 till late and food is served from 12:30 till 9:30
Doña Pepa, Ciudad Quesada (+34) 966719023
 
La Pizza Nostra
Recommended by Keeley Carwich
This one is a real family favourite restaurant. Aside from the fact that all kids love pizza, the atmosphere is great and there is also a varied menu if you dont fancy Italian.
Plaza Castelar 6, 03180 Torrevieja (+34) 965710033
 
Pizzabona
Recommended by Stella Robins
If you dont fancy eating out with the kids then you cant go far wrong with takeaway or pizza delivery!
C/Antonio Machado s/n, 03180 Torrevieja (+34) 966702153
 
Emerald Isle Complex
Recommended by Stella Robins
The Emerald Isle Complex is located on the La Florida urbanization on the Orihuela Costa. There is a fantastic restaurant there with a good menu (breakfast, lunch and dinner) and a kids menu for under 5 euros. 
Urb La Florida, Los Altos, Orihuela Costa / Torrevieja (+34) 647 681 294www.costablancaemerald.com
 
Amsteleria in Quesada
Recommended by Keeley Carwich
The Amsteleria in Quesada is definitely for mums and dads who enjoy a few beers! There is a pump on each table and you can serve yourself but pay at the end (very dangerous!!!). For the children there is a soft play area and bowling area.  They also host children’s birthday parties.  They serve Tapas in the bar downstairs and have lots of snacks and Menu del Dia on offer.
Avda. de las Naciones, 13 Ciudad Quesada, Rojales (+34) 966719475 www.laamsteleria.eu
Comments:
"For once in your life your kids will be begging you to take them to the pub and be happy to leave you to enjoy a few beers! There is a mums and toddlers group that takes place there on Tuesday mornings at around 11am." (KC, June 09)