Depends on how you define "reasonable" - parking lots/garages anywhere in midtown are going to be pricey so "reasonable" is going to be a relative term. As a general rule "open-air lots" are slightly less expensive than covered garages but the emphasis is on the word "slightly". You'll find parking lots/garages on just about every block in the area (sometime even 2 or 3 on the same block). Another thing to consider many of the lots are small and get filled up quickly by both monthly contract parkers and people working in the area so it's not always possible to park in a specific lot on a given day. Also, a great many of the lots are operated by the same company so rates are very similar from lot to lot.

FYI - All lots/garages are required to conspicuously post their rates so you'll have no trouble figuring out the cost before you park.

You won't find any (well, at least not many) parking "lots," though they certainly exist (there's one around the corner from me at the corner of 2nd Avenue and 36th Street, near the entrance for the Midtown Tunnel. The streets around Times Square are filled with garages, however. Expect to pay about $25 to $35 to park for the day on a Sunday. If you want to know the exact locations of garages, one big company is Icon Parking. THey have a web site and list their garages on the site.

If you are driving into the city and aren't really that familiar with it (and especially if you are just coming for the day), it might be worth your while to park outside of Manhattan and take public transportation into Manhattan. There is parking near all the ferry routes across the Hudson from New Jersey if you are coming from the west, and there are parking garages (easily used on Sundays) in White Plains and other cities to the north.

It will cost you more to take public transportation into Manhattan and park, but it might be a bit easier.

Go to www.nyc.bestparking.com - it's discounted parking rates for garages. All you have to do is fill in the date and hours you will be there and you can print off a coupon! Easy!

Also, street parking is mostly free on Sundays in Manhattan, but you'll probably have a tough time finding any close to Times Square. If you're happy to walk a couple of blocks, you should be able to find some further east of FAO.

Best tip for driving on a Sunday in the city though is arrive early! Traffic can get crazy in the early afternoon - plus most garages have an early bird special for $12-15 if you arrive before 10am.

On almost every weekend there is a street fairs and maybe a parade as well.

Here are the advisories from this weekend. I do not know when they will post the advisories for next weekend.

http://www.nyc.gov/html/dot/html/motorist/wkndtraf.shtml

It's vital to check out the parades and street fairs - since this will have a huge effect on both driving and parking. Go online, pick a garage in advance and make a reservation - and that way you know exactly where you're going and what it will cost. Plan on at least $30 for the day. And do NOT assume you can park on the street anywhere. There are places to park in residential area side streets - but not where you would be going - and it might take 20 to 30 minutes driving around to find a spot.

I'm a big fan of parking at Port Authority bus station, where you enter and exit right at the tunnel.

There is one big advantage to driving into the city on a Sunday: You don't have to feed the meters, so you can park for free!
If you come in before 11, the chances are excellent for finding a space on the West Side, say in the upper 30s, which is very close to Times Square and within walking distance of your other stated destinations. I speak from experience, when I say the chances are excellent. We do it all the time!