First, I assume you are flying so check airfares to Logan and Manchester NH as well. A lot of times. MHT is cheaper than Portland. It's about a two hour drive.

It would be tempting to have a car to drive around to some other places in Maine esp beaches if it's a warm weather honeymoon. Maybe rent for just a day or two.

You might be surprised by the price of restaurant eating in the Northeast, I think $1000 for two people/6 days might be low esp if you want to order wine/alcohol.

You can do low budget things, maybe one expensive meal. Don't go too cheap on the hotel, you don't want to stay by the airport/south Portland. Do a search for old posts about Portland and recommend hotels. The last time we stayed at a condo in Wells but that's a long drive from Portland and not a place I would recommend. You can look at some menus on the internet so see what you would spend if you went to an expensive restaurant like Hugo's or Fore.

When will you be going? While there are year-round attractions in Portland and in surrounding towns, some things are seasonal (often only open from Memorial Day to Columbus Day). Summer is the best time to be in Maine unless you ski, but it's also high season with commensurate hotel prices.

Maine is really best experienced by car, Portland for six nights might get a little boring. Hertz usually has a coupon on their website that negates the under-25 charge, but you do need to have your own insurance or a credit card that covers car rental insurance. Inn By The Sea in nearby Cape Elizabeth would be great for a couple of nights!

Portland is a fun little city, but a week there might be a bit much, unless you rent a car for at least part of the week. There are some truly beautiful seacoast towns both north and south of Portland. Time of year is a big factor for visiting Maine - June thru September are ideal.

You can take Amtrak Downeaster from Boston North Station to Portland for less than $50 for the 2 of you. Boston North station is only about 2.5 miles by taxi from Logan through the tunnel. The Portland Amtrak station is across the river from the Portland airport. The train takes about 2.5 hours.
There are 2 trains each morning. The late afternoon and evening trains would not be so good.

Will second the Amtrak Downeaster, though note that the Portland station is a very long way from downtown (there likely is a city bus that connects to downtown, though). This train also stops in Exeter, NH (a nice town to visit for the day), Wells (in summer, there are buses/trolleys that connect from there to the Kennebunks and Ogunquit), and Old Orchard Beach (seasonal stop only).

A car is useful though, and if you want to visit things like the Kittery Outlets or Old York Historical Society buildings or Seashore Trolley Museum in Kennebunkport, it will be necessary.

I agree with various comments above.

Here's a sugge4stion:

Fly in Portland and stay a few nights. You won't need a car while in Portland, though it's not too inconvenient if you DO have one while there. Price it both ways - a weekly rental starting and ending at the airport may be cheaper than 4 days picking up downtown and returning it to the airport.

After a few days (if you don't already have it), RENT A CAR and head up the coast for the next few nights. Lot's of options - mid-coast might be most convenient. Maybe Camden?

Depending on what time your departing flight leaves, you may want to stay in Portland your last night.

IMO, you want to fly in Portland - even if it cost a bit more. If it were me, I would skip one fancy meal out to save the budget instead.

I like Portland, but as others have noted, you may want to ue it as a base to see other places. Thus, a car might be necessary, or you will have to join (and pay for) organized tours.

Also, I second the idea of staying near the east/shore end of the city rather than the west end/airport side.

Depending on time of year, your budget could be a little tight, mainly because accommodations could be a bit expensive in summer. "How much spending $?" is hard to answer. What are your dining habits? What attractions do you want to see?

But let's say you have $3000 for 6 nights.
$1200 for lodging
$400 for car rental
$1400 for meals, etc.