A quick overview of some Neopets features that may help you out in getting nice items or NP.
Dailies
The Giant Omelette -
Located in Tyrannia Plateau, and can give your pet a yummy omelette once per day - that can last a whole 3 bites!
The Giant Jelly -
Located in Jelly World (it really *does* exist =o!) and by visitng you can get a delicious jelly day by day :)
Tombola -
This nice activity in Mystrey Island can give you anything from Faeries and Codestones to Random Items.
Deserted Tomb -
In this somewhat new feature located at the lost city of Geraptiku, you can get a whole variety of Island Items and even an avatar, though at the risk of harming your pets HP a bit.
Coltzan's Shrine - Increase in pet stats, Dubloons, Desert Food etc' is what you get if you try going to the Lost Desert shrine.
Healing Springs - Healing your pets and giving out Healing Potions is what this Water Faerie does best.
Snowager - If you're up for an exciting ride, check out the Snowagers Lair and try to get Keyrings,
Neggs, or an Icy Blast (and if you're lucky, an avatar to go with it ;))
Wheels
Wheel of Excitment - You can get anything from 10k with an av to the mystrey prize of 31 NP with this wheel. It costs 150 NP to play every two hours.
Wheel of Knowledge - a somewhat pricey wheel at the range of 500 NP and a chance to spin it once per day, not a very appealing choice on most parts,
though it could get you a rare avatar or a nice item from time to time, it's mostly not worth it.
Wheel of Mediocrity - Only 50 NP a spin, and you can come back every 40 or so minutes.
This wheel can also get you an avatar, but with a low price also comes the opprotunity to win less-vauled items or harming your neopets with fiery showers.
Wheel of Monotony - Perhaps the most tiring wheel of them all, it costs 100 NP to play and can spin anywhere from a couple of minutes to a couple of hours, bordering with days. The prizes from this wheel though are quite nice a lot of times,
you can win a paint brush, a Mazzew and an avatar from it!
Wheel of Misfortune - The name probably says it best. For 100 NP you can get your pet get sick, a stolen item or NP or... You guessed it, an avatar.
Quests
Brain Tree - to complete his quest you must complete 2 of the Esophagors quest for the answer,
however he might give you the wrong data sometimes. The Brain Tree can give you nice items depending on the level of the quest you're currently on - the higher the level, the nicer the prize (usualy).
Ednas Tower - Edna usualy asks for fairly cheap items, but she also gives cheap items in return - most of her quests are a waste of time,
though if you're an avatar collector - she gives a spiffy avatar out randomly in one of her quests (though it usualy takes quite a few).
The Esophagor - Feeding this beast can be proven both easy and hard tasks. He usualy has the same range of item requests as Edna,
and at times his prizes may be quite nice as well though sometimes it'll be just junk.
Kitchen Quest - He can ask a variety of items, and from time to time give nice things back, though as with every quest - its a bet.
Illusen's Glade - Illusen's quests go by level - with every level the prize is nicer and at the 20th you can even get an avatar - yet if you fail one,
you go straight back to the begining. It's a risk you'll have to take, and up to you to think if its worth it or not, but just incase have enough NP ready on the side, as its a timed quest ;)
Jhudora's Cloud - With the same basic principals of Illusen's Glade of time and levels (though she'll never admit it) you can get a whole bunch of Evil Faerie
items for this Dark Faerie.
Snow Faerie - The snow faerie can ask for a whole lot of different things, at times pricey, but her gifts are rumored to give quite rare items every so often :)
In conclusion, most wheels and quest can be proven as a big waste of time and NP, but if you're an avatar collector or just seaking for thrills, it's your choice to make.