I bought the LX, it has 15-inch wheels with ugly wheel covers.

1. What upgrade options are available if I want to keep my tires?
2. If I were to change to 16-inch wheels, would the car ride better? Rougher ride? Handle better? Just look cooler?
3. How much would it cost to upgrade the wheels in cost/labor?

 

1. go to the tire manufacturer's website, look up the model and size, and it will tell you the range of wheel widths that tire will fit. normally, the stock width is probably 6" or less, but if you are able to go with a wider rim, you will need to get an appropriate offset. if not going wider, get a rim offset closest to stock if possible.

2. if you go with 16s, the aspect ratio/tire height/sidewall will not be that much smaller so the ride should be similar. since there is less sidewall, there will be less flex so handling should seem to be improved. of course if you get higher speed rated tires, the compound is usually better (ie, stickier) so handling will be better.

3. cost of wheels + the cost of removing the tires off the stock wheels + remounting them on the new wires + moun/balance/valve stems on either wheel or both

 

if you wanna use the same tires you can only get a rim that is 15". a 15" tire will not fit a 16" rim or any other size rim other than 15". i'm not sure of the width of stock rims but i believe they are either 5.5" or 6" wide

a 16" rim will handle better only if you get a wider rim. like say 16x6.5 or 16x7. then you can go with a wider tire. the wider the tire the better they will handle. it will ride a little rougher but nothing that you will notice. now if you go with a 17"-19" then you will notice a difference

if you go with a 16" rim/tire package you can get them for around $600-$1000 depending on what you get

check out
www.wheelmax.com
www.wheelmart.com
www.tirerack.com (i think they just have tires)
www.groupbuycenter.com

for the rims. i believe the bolt pattern on the 2003 Accords are still the same. so if its a V6 its 5x114 and the I4 is 4x114 (some may have them listed as 114.3 but its the same thing)

 

You won't get that noticeable of a handling improvement on 16" wheels, especially if the car remains sprung at the stock height and the springs carry the stock load stiffness.

I'd recommend going to a 17" inch wheel (maybe even Honda's optional OEM 17" tire) and adding accordingly sized rubber.