The new uniform manual is referenced below. It's also found on Homeport at this link. Below are some of the quick reference for cadets. Scroll down for information on boots and shoes.

Sea Cadets

NSCC CADET FLASH, CHEVRON AND RATING BADGES

League Cadets

NLCC CADET FLASH, CHEVRON AND RATING BADGES

Boots and Shoes

The division has a limited supply of dress shoes and boots. Most of them are used and may look acceptable on the inside, but the insoles and soles are well worn. We recommend that families buy a comparable shoe and boot. Cadets may have dress shoes already at home that could comply with regulations. Please send a picture of them so we can see if they comply.

Dress Shoes

Official uniform specifications: "Worn by NSCC/NLCC cadets. Plain toed, oxford style black, low quarter, lace shoe, made of smooth leather (No synthetic high gloss material). The heel shall be an outside heel 3/4 inch - 7/8 inch high with a flat sole."

Here a couple of stores where similar looking shoes can be purchased at a reasonable price. Amazon, Walmart, etc. may also have good deals.

Galls.com. Search for "leather oxfords". Recommended options listed below. Not exact match to Navy style but better priced. Bates (previous Navy vendor) and Altama (new Navy vendor) are very expensive. For comparison the cheapest price at the official Navy Uniform store is currently $63.18. These can only be ordered by military personnel.

Option 1. Option 2. 

Rothco.com. Same comments as above.

Option 1.

Boots

Official uniform specifications: "Black all leather safety boots (steel toed) are the standard boots worn with the Navy Working Uniform (NWU) Type III, and Type I while shipboard or at trainings with environments mandating safety shoe wear. Authorized black boots include 9-inch or 8-inch high boots"

Boots are a bit more complex to find. They need to be leather (for shining) and you should avoid if possible boots that have zippers, mesh sides, big treads ("jungle boots"). Ask around with other cadets to see where they have found similar boots. 

Galls.com. Search for "leather boots" or "combat boots". Some options are listed below. Not exact match to Navy style but better priced. Bellville (Navy vendor) are very expensive. For comparison the cheapest price at the official Navy Uniform store is currently $101.17. These can only be ordered by military personnel.

Rothco.com. Same comments as above.

Military Uniform Supply.