hey sara - there are many great places in lahore that you can visit but got to have the time for it. I don't how much time you have in lahore but i'll just list some of the places that you could visit.
cafe aylanto: Probably the best restaurant with great food and fantastic atmosphere. Its located on m.m alam road gulberg. It is kinda expensive but believe me its absolutely worth it.
dynasty restaurant: Again a great restaurant. I think its the best chinese restaurant in lahore. It is in avari hotel which is on mall road.
m.m alam road: This road is full of restaurants and shops. It is in gulberg, ask anyone they'll guide u to it. It is a long road full of shops and then once this road finishes you hit a roundabout, take a left from that roundabout and you'll find many cool cafes for example, world of fashion cafe, cinnabon, coffee tea and company, gloria jeans etc. You will also find a mall called xinhua mall there where you can do some shopping.
mall of lahore and fotress stadium: Mall of lahore is in cantt. And it is a new mall with a beautiful building. Try going at night because the building looks beautiful from outside once it is lit. This is another mall you can find some good shopping. Fotress stadium is another good place to go for shopping. It has clothes, food, fun places, cd shops etc.
liberty market: Another very popular place in lahore gulberg where hundreds of women go everyday to shop. For some, it is their favorite place. You should definitely go check it out.
d.h.a: Its a residential area, probably the best one in lahore. There are a lot of shopping there too and also a lot of restaurants (lahoris are crazy about their food). Go to y block or h block market and you'll find everything you are looking for.
landmarks: There are many landmarks in lahore but to be honest i am not an expert when it comes to landmarks. You could go the badshahi mosque (absolutely beautiful at night) and if do go, you have got to go to coocos nest. It has an amazing view plus amazing food too. Other than badshahi mosque, you could go to shalimar gardens, lahore fort and all. You can find these places online too.
But one thing that you have to keep in mind is the weather. I think karachites are used to the breezy weather. Lahore has crazy hot humid summers and people usually don't hangout during day time, especially in landmarks mentioned above. You are lucky however that the weather these days is very pleasant because of the monsoon rains.
Regarding the gift, as you go around and check some of the places listed above, you'll find dozens of options! So don't worry about the gift you'll eventually find a great one! Have fun in lahore and i hope this helps you!