There are no published 5e Forgotten Realms supplements as of yet, and they have changed the Realms a good bit with each new edition. If you don't care about "keeping up with the new timeline," the most supported classic starting location is far and away:
Shadowdale
Sourcebook and Adventure Coverage
This town in the Dalelands is given some detail in the AD&D 1e "grey box" Forgotten Realms boxed set; in the revised boxed set this is expanded to a 96-page book specifically about that town with an intro adventure, it is the default FR starting town for that edition. Greenwood's own home campaign clearly spent a lot of time in the Heartlands (Dalelands, Cormyr).
Shadowdale just got normal coverage in the 2e Forgotten Realms Adventures hardback but still a lot of adventures from this period (FRQ series, the Sword of the Dales trilogy, Four from Cormyr, the Godawful FRE series, etc.) were set in and around Dalelands and Cormyr, and eventually Volo's Guide to the Dalelands gave all the background again for 2e. Daggerdale gets a lot of treatment too. But from a general point of view of 1e and 2e Realms content, this is the area that is by far the most detailed and most supported with adventures and other products.
3e FR content doesn't really hit on any area specifically more than another; Shadowdale does get blown up for a bit in a sourcebook/adventure (Shadowdale: The Scouring of the Land).
In 4e, they focused instead on the "Neverwinter Campaign Setting" and Neverwinter as a starting city with setting and adventure support - Neverwinter and Baldur's Gate got a lot of attention over time because of the computer RPGs set there of course. This involved a bunch of changes ("The Sundering"), but they reset the Realms in 5e using standard comic-book parallel worlds stuff to the 3rd edition geography, so ironically you may find these newer products less useful. Though Cormyr and the North were actually some of the least-touched parts of the 4e changes, so you may be able to port stuff.
Campaign Hub Appropriateness
Shadowdale is suitable for starter parties (and was specifically tooled for it in its sourcebooks) but because Elminster and other high level folks live there, it is also suitable for high level play. In most campaigns you'd end up going to a big city to get bigger magic, meet more important people, etc., but in your campaign they'll never leave. Shadowdale is optimal from that point of view - the adventure support in the Dalelands goes from low to high level, and the high level mover-and-shaker NPCs allow even high level parties to have meaningful interactions there.
Downsides
The only downside is really that Shadowdale is VERY well detailed... In the 2e boxed set every farm in the area is detailed - and having high level NPCs like Elminster around may crimp your style if your campaign doesn't account for them running to him trying to get help every time they get out of their depth.
Summary
So if you are looking for a well mapped and supported starting town, there is no better answer than Shadowdale in the history of FR products... There's a lot of other choices, but this one is easily covered with 5x the detail of the next comer, especially if you're excluding big cities like Waterdeep that have sourcebooks in a couple editions.
Are there any unforeseen issues with changing the weapons like this?
Yes
The unforeseen issue is that you create the impression in the minds of the players that Waterdeep guards are an ad-hoc militia rather than an organized, standing force.
Efficient and effective state-run military/police have standardised equipment - uniforms, armour, ancillary equipment and weapons. Para-military militias have whatever they turned up with. Waterdeep guards are the former - you run the risk of making them look like the latter.
There is nothing wrong with them carrying spears and maces and daggers and choosing the appropriate weapon for the task at hand but they should all be uniformly armed.
Basically, Waterdeep guards look like this:

Not this:

As an aside, the overwhelming majority of weapons ever used in the pre-firearm age were spears for the obvious reasons: they're cheap, can be made by anyone (a basic spear is a stick with a point) and all the nasty stuff happens 6 to 12 feet away from the guy holding it.
Best Answer
Waterdeep is approximately 3.8 miles x 1.5 miles
Or ~20,000 feet north/south and ~8,000 feet east/west. Both measurements were done along the greatest straight-line dimension of the city. This measurement is done by measuring the space between the walls of Waterdeep, so it includes the enclosed section of the harbor to the south.
This was derived from the map provided in the 3rd edition book City of Splendors: Waterdeep, which actually includes a scale. A copy of this map can be found here if you would like to make more precise measurements of distances between things.
I checked other sources that relate to Waterdeep, such as Volo's Guide to Waterdeep (2nd Edition), and did not find any contradicting maps. The 2nd Edition adventure titled Waterdeep includes a map, but no scale. The 1st edition sourcebook Waterdeep and the North does the same...map, but no scale.
Thus, with no contradicting evidence, it's probably a fair assumption that the 3rd edition scale of the city is accurate.