It depends on the sites to visit and the traveling pace,
but I would add one day for Nikko,
especially when I am likely to be there
during the autumn coloring of the foliage in a good weather.
We know that some of these destinations are not covered by the JR pass Depending on how the rest of your itinerary is,
Japan Rail Pass or JR East area pass might be a good choice.
For your two side trips from Tokyo,
Marugoto Nikko-Kinugawa Tobu Free Pass sounds suitable.
https://www.japan-guide.com/e/e2358_002.htmlWhile the three other passes shown below
are available exclusively to foreign travelers,
this pass is issued regardless of the nationality of passengers.
Around 11800 yen
(i.e. 9490 to 9590 yen + about 2300 yen)
as transportation cost for the two side trips.
: About 300 yen as railway fees
to get to and back from (Tobu) Asakusa Station (#).
: 6150 yen
on Marugoto Nikko-Kinugawa Tobu Free Pass,
which covers the fees shown below as (A) through (C)
and Tobu Bus Nikko fares for your rides on Day 4.
(#) You can buy the pass
which is valid from another Tobu station.
: 1340 or 1440 yen (depending on dates)
as Tobu Railway Limited Express surcharge
for your ride on Day 3 to Shin-fujiwara Station.
: 370 yen
as Yagan Tetsudo Railway Limited Express surcharge
for your ride on Day 3 to Yunishigawa-onsen Station.
: 1030 yen
as Tobu Railway Limited Express surcharge
for your ride of a specified train
in the afternoon on Day 4 for Asakusa.
: About 2000 yen as railway fees
to get to and back from Kamakura Station.
: 600 yen
on Enoshima Electric Railway [Enoden]
"Noriorikun" one-day pass.
(A) 2 x 150 yen
as Tobu Railway basic fares
for Kinugawa-onsen Sta. -- Shin-fujiwara Sta.
(B) 2 x 510 yen
as Yagan Tetsudo Railway basic fares
for Shin-fujiwara Sta.
-- Yunishigawa-onsen Sta.
(C) 2 x 880 yen
as Nikko Kotsu bus fares
for Yunishigawa-onsen Station bus stop
-- Honke Bankyu Ryokan Mae bus stop
Tobu NIKKO PASS all area (4520 yen, 4 consecutive days)
does not cover the fees shown above as (B) and (C)
(2780 yen).
This pass brings you a discount of about 20 percent
(460 to 480 yen) on the Tobu Limited Express surcharges.
http://www.tobu.co.jp/foreign/en/pass/all.htmlSo,
compared to when you use the Nikko-Kinugawa free pass,
the amount of the cost is estimated
at higher by 690 to 670 yen.
(4520 - 6150 - (460 to 480) + 2780 = 690 to 670.)
JR TOKYO Wide Pass (10000 yen, 3 consecutive days)
covers JR fees to go between Tokyo and Kamakura
(except on the Tokaido Shinkansen)
and Limited Express surcharges
for rides of JR-Tobu through trains,
while it does not cover
Tobu Bus Nikko fares
or the fees shown above as (A) through (C) (3080 yen).
Greater Tokyo Pass (7200 yen, 3 consecutive days)
does not cover
surcharges (to be paid in addition to the basic fares),
Tobu Bus Nikko fares
or the fees shown above as (B) and (C) (2780 yen).