Where are crafting stations the closest to a Trading Post representative?

The Royal Terrace is has crafting stations closest to a trading post, followed closely by Havoc's Heir. Both of these require admission passes that can be purchased in the gem store (when available), though, with the permanent version of each costing 1000 gems.

The closest free trading post to crafting stations is in Rata Sum, by Accountancy Waypoint. With the crafting stations placed symmetrically around the trading post, bank, and guild bank, this area is especially convenient. The trading post in The Grove is also close to the crafting stations, but some more so than others.

The crafting stations in the citadel of your home borderlands in WvW are also a convenient place for crafting, assuming there's no queue to get in, because going there and back doesn't cause you to lose your position in PvE or cost waypoint fees.

If you're only concerned with convenience for a short duration, it might be worth using a Trading Post Express, which are typically received from achievement rewards and daily rewards, but can also be obtained from the gem store.