I highly suggest trade.secureae.com. A simple online NXT wallet with the Asset Exchange front an center.
If he's not comfortable leaving assets on an exchange, he might not be comfortable with online services either
It is 100% client based code and everything that happens happens on the blockchain. So, you can always just use your account on a local NRS wallet if you want. Nothing ties you to the service in any way.
This is much different than an exchange where you coins and assets are nothing more than a database entry.
I will always hold the bulk of my coins and assets in my accounts on the relevant blockchain. (not technically on my computer).
The blockchain is a ledger of all the transactions that have happened on a coins network. It uses a concept called event sourcing. Basically, anytime something happens a new "record" is added to the database, rather than it modifying existing data. To determine the current "state" of any account/address you start from the beginning and look at all the events that occured for that account.
So, your coins are in this ledger. If you don't download the blockchain your coins aren't really "on your computer". If you use Electrum for example, it doesn't download the bitcoin blockchain. So, the coins aren't "on your computer". I know it is semantics, but as a dev I tend to be a bit pedantic about tech stuff.
I have never downloaded the bitcoin or via blockchains, so my coins aren't really on "my computer". That's what I was saying. This is why web wallet, vs lightweight wallet vs native wallet is really more a preference thing. I like being able to walk up to any computer and login into my blockchain.info wallet. Also, like being able to use my phone to spend from that wallet, rather than having my mobile wallet be a separate set if keys from a qt wallet on my PC.
