Non alcoholic drinks are always a matter of preference. I personally like the sparkling drinks and the lemonades. I found a few links, but more importantly recipes. I drink lemonade, and coconut and pineapple drinks.

Here is a great collection of some non alcoholic ones:
http://www.drinksmixer.com/cat/8/

Here are some pineapple drinks. My favorite is the coconut punch, so give it a try, it's easy to make!

http://www.tasteoftx.com/bevs/non/coconut.html

If you like teas:
http://stanford.wellsphere.com/wellpage/tea-recipes

Here's some quick ones that are very good. A good ginger ale is nice on New Years! Antioxidants are healthy, so why not a healthy alternative?

Sparkling Antioxidant Non-Alcoholic New Year Drink Recipes

Ginger-Apple-Fizz; Take 1/4 inch slice of ginger root and 1 apple (seeded) , put through juicer. Top with sparkling water. Garnish with lime, lemon or orange.

Ginger has long been known to aid digestion and improve immunity. Apples also aid in digestion and contain vitamins B & C,. This recipe could be suggested for people with arthritis, gout and rheumatism.

Ginger-Berry-Blues; Take 1 quart of blueberries, a medium bunch of grapes and 1/4 inch slice of ginger root, put through juicer. Top with sparkling water. Garnish with lemon. lime or blueberries through a skewer.

Blueberries have anti-cancer and anti-bacterial properties. Grapes contain vitamins A, B & C and calcium. Blueberries, grapes and ginger are all good for arthritis (rheumatoid), making this cocktail great for people who suffer from this degenerating disease.

Ginger Ale: Take 1 lemon wedge, 1/4 inch slice of ginger root and a medium bunch of green grapes, juice lemon, then ginger root and grapes. Top with sparkling water. Garnish with lemon or lime.

If you like fruits, a fruit shake is very delicious!

Fruit Shake Ingredients
1 cup fruit Yogurt
1 Banana
4 oz frozen Orange juice
1/2 piece textural Fruit (apple, pear, pineapple)
6 Ice cubes

If you like lemon and tea:

Arnold Palmer Ingredients
5 oz Lemonade
5 oz Iced Tea

If you like a cocoa and vanilla combo, milky treat, the Dutch Treat is excellent!

Dutch Treat
2 cups Milk
2 tblsp carob or Cocoa powder
1/2 tsp Vanilla extract
2 tblsp Honey
1/2 tsp Cinnamon

If you like grapes, this is great!

Great Grapes Ingredients
1 cup Grape juice
1 cup Soda water
1 tblsp Honey
1 tblsp Lemon juice

I host a popular and (hopefully) well received New Years party every year.

I make 3 very large punch bowls of clearly marked non-alcoholic punch and place them on the bar with all of the other liquor. I've chosen and refined these 3 punches because they taste good and when mixed with Rum, Whiskey or Vodka make a good alcoholic alternative.

Lemonade & Strawberry Based:
3 (6 oz.) cans frozen lemonade (not pink), thawed (18 oz. total)
1 (10 oz.) pkg. frozen strawberries with juice
1 qt. Ginger ale
Serve with lots of ice

Cranberry Based:
2 oz. cranberry juice
1/2 oz. lemon juice
1 oz. orange juice
2 oz. ginger ale
Serve with lots of ice

Warm Cider Punch:
1 (12-oz) frozen cranberry juice
1 (6-oz) frozen lemonade
1 (12-oz) apple juice concentrate (thawed & undiluted)
9 C. of water
5 (3-in) sticks of cinnamon
6 whole cloves
1 tsp. of ground nutmeg
1 C. of sugar
Bring to boil in large pot.

If your guests don't drink alcohol, they likely aren't going to expect drinks that are non-alcoholic versions of alcoholic drinks, so don't sweat trying to come up with them. You can have fun with these, which I've served many times to various groups of people of all ages:

Italian Sodas:

Sparkling Water (not tonic water) or Seltzer Water. Many groceries sell these in 2-liter sizes
Coffee Flavoring Syrup: Torani's and DaVinci's are most widely available, but there are other brands, including Starbucks. Fruit and candy flavors are best for this. Include at least a couple of sugar-free varieties.

This is simple: Just add a shot of the coffee syrup over ice cubes in a 12 to 20 ounce glass, and fill with chilled sparkling water! Torani's Black Cherry is delicious this way.

You can also used liquid flavored stevia drops in place of the coffee syrup, according to the amounts listed on the bottle. Chocolate Raspberry by Sweetleaf Stevia is great!

Farmer's Soda

Follow the above recipe, but fill the glass halfway with milk or cream before adding the sparkling water.

Sodas Tortuga

Fit for Jack Sparrow!

In a 20-ounce glass:
One dip ice cream--fruit flavor or vanilla
one half cup of: pineapple juice, OR pineapple orange juice, OR (the best) Trader Joe's Italian Blood Orange juice (Yaarrrr, matey! Blood and thunder!)

Top it up with sparkling water. You can have a lot of fun with this: orange sherbet with passion/orange juice; vanilla with blood orange; pomegranate with tangerine/lime.

Pomegranate seeds sprinkled on this look like little jewels and taste great!

And no one will ask why the rum is gone.

If you only want cocktail recipes, you can find a bunch of delicous one here (with great pictures that let you know in advance what they´ll look like):

http://www.greatcocktails.co.uk/NonAlcoholicCocktailsCategory.html

What about alcohol-free sangrias? They are always great at parties. Find a recipe for a sangria, and replace the wine with grape juice and voila, you're done!

I found this page with a variety of sangria recipes.

Here is a drink recipe I found for mock Champaigne

http://www.floras-hideout.com/drrecipes/recipes.php?page=drrecipes&data=k-p/Mock_Champagne

there are more drink recipes at this website so you can look around and choose what you want.

Anything with a tangy zingy flavor. Also, the alchoholic drinks always look so fancy, it is a nice touch to make the non-alc drinks as attractive to the eyes as their counterparts. You can freeze intensely flavored (sweetened) juices like lime, lemon, strawberry and mango in ice cube trays. Then when the drinks are served, you can blend them up individually by the serving. Just add the frozen cubes to more of the same juice and blend. Garnish with citrus zest, lemon slices, maraschino cherries, etc. Another yummy option is to use sherbet instead of freezing juice yourself. Just add the juice or soda to the sherbet and blend. It can be made by the bowlful, and you can get really creative! mountain dew and lime sherbet, 7up and lemon sherbet, and this sounds weird, but it is really yummy-- Dr. pepper and raspberry sherbet.

How about something that resembles champagne, but is not champagne? like sparkling apple cider (non-alcoholic)
http://www.martinellis.com/products/sparkling/