Im a lahori but dont know about good economical hotel to stay in.. sorry for that
you can ask @engineermali
or look for his thread, he visited lahore fews months back.
but nice places to visit may involve but not limited to:
Fortress stadium (hyperstar, joyland, and many restaurants)
Mall raod
lahore Zoo
Wahga border
Food street
Liberty
MM alam raod for numerous restaurants
race course park (jilani park)
Y block DHA
Regarding minar-e-Pakistan and badshahid masjid, there is huge construction going on there, so look for alternate routes before visit.
Sozo park is flop place for family. Nothing special there. Also if you wanna enjoy movie, then cinestar cinema in township or bahria cine gold (better option) are also there.